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2026-01-01
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2026-02-28
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<p>Last updated on<strong>August 5, 2025</strong></p>
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<p>Last updated on<strong>August 5, 2025</strong></p>
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<p>If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in various fields such as vehicle design, finance, etc. Here, we will discuss the square root of 1029.</p>
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<p>If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in various fields such as vehicle design, finance, etc. Here, we will discuss the square root of 1029.</p>
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<h2>What is the Square Root of 1029?</h2>
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<h2>What is the Square Root of 1029?</h2>
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<p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 1029 is not a<a>perfect square</a>. The square root of 1029 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √1029, whereas \(1029^{1/2}\) is in exponential form. √1029 ≈ 32.085, which is an<a>irrational number</a>because it cannot be expressed in the form of p/q, where p and q are<a>integers</a>and q ≠ 0.</p>
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<p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 1029 is not a<a>perfect square</a>. The square root of 1029 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √1029, whereas \(1029^{1/2}\) is in exponential form. √1029 ≈ 32.085, which is an<a>irrational number</a>because it cannot be expressed in the form of p/q, where p and q are<a>integers</a>and q ≠ 0.</p>
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<h2>Finding the Square Root of 1029</h2>
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<h2>Finding the Square Root of 1029</h2>
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<p>The<a>prime factorization</a>method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where long-<a>division</a>method and approximation method are used. Let us now learn the following methods:</p>
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<p>The<a>prime factorization</a>method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where long-<a>division</a>method and approximation method are used. Let us now learn the following methods:</p>
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<ul><li>Prime factorization method</li>
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<ul><li>Prime factorization method</li>
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<li>Long division method</li>
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<li>Long division method</li>
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<li>Approximation method</li>
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<li>Approximation method</li>
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</ul><h2>Square Root of 1029 by Prime Factorization Method</h2>
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</ul><h2>Square Root of 1029 by Prime Factorization Method</h2>
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<p>The<a>product</a>of prime<a>factors</a>is the prime factorization of a number. Now let us look at how 1029 is broken down into its prime factors:</p>
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<p>The<a>product</a>of prime<a>factors</a>is the prime factorization of a number. Now let us look at how 1029 is broken down into its prime factors:</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 1029 Breaking it down, we get 3 x 3 x 3 x 7 x 17: \(3^3 \times 7 \times 17\)</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 1029 Breaking it down, we get 3 x 3 x 3 x 7 x 17: \(3^3 \times 7 \times 17\)</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 1029. The second step is to make pairs of those prime factors. Since 1029 is not a perfect square, therefore the digits of the number can’t be grouped in pairs.</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 1029. The second step is to make pairs of those prime factors. Since 1029 is not a perfect square, therefore the digits of the number can’t be grouped in pairs.</p>
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<p>Therefore, calculating √1029 using prime factorization is not feasible for finding an exact<a>whole number</a>.</p>
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<p>Therefore, calculating √1029 using prime factorization is not feasible for finding an exact<a>whole number</a>.</p>
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<h2>Square Root of 1029 by Long Division Method</h2>
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<h2>Square Root of 1029 by Long Division Method</h2>
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<p>The<a>long division</a>method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the<a>square root</a>using the long division method, step by step:</p>
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<p>The<a>long division</a>method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the<a>square root</a>using the long division method, step by step:</p>
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<p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 1029, we need to group it as 29 and 10.</p>
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<p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 1029, we need to group it as 29 and 10.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is closest to 10. We can say n as ‘3’ because \(3 \times 3 = 9\) is lesser than or equal to 10. Now the<a>quotient</a>is 3; after subtracting 9 from 10, the<a>remainder</a>is 1.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is closest to 10. We can say n as ‘3’ because \(3 \times 3 = 9\) is lesser than or equal to 10. Now the<a>quotient</a>is 3; after subtracting 9 from 10, the<a>remainder</a>is 1.</p>
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<p><strong>Step 3:</strong>Now let us bring down 29, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number: 3 + 3 = 6, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 29, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number: 3 + 3 = 6, which will be our new divisor.</p>
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<p><strong>Step 4:</strong>The new divisor will be the<a>sum</a>of the dividend and quotient. Now we get 6n as the new divisor; we need to find the value of n.</p>
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<p><strong>Step 4:</strong>The new divisor will be the<a>sum</a>of the dividend and quotient. Now we get 6n as the new divisor; we need to find the value of n.</p>
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<p><strong>Step 5:</strong>The next step is finding \(6n \times n \leq 129\). Let us consider n as 2; now \(6 \times 2 \times 2 = 124\).</p>
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<p><strong>Step 5:</strong>The next step is finding \(6n \times n \leq 129\). Let us consider n as 2; now \(6 \times 2 \times 2 = 124\).</p>
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<p><strong>Step 6:</strong>Subtract 124 from 129; the difference is 5, and the quotient is 32.</p>
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<p><strong>Step 6:</strong>Subtract 124 from 129; the difference is 5, and the quotient is 32.</p>
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<p><strong>Step 7:</strong>Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 500.</p>
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<p><strong>Step 7:</strong>Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 500.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 642 because \(642 \times 1 = 642\).</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 642 because \(642 \times 1 = 642\).</p>
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<p><strong>Step 9:</strong>Subtracting 642 from 5000, we continue the process further for more precision.</p>
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<p><strong>Step 9:</strong>Subtracting 642 from 5000, we continue the process further for more precision.</p>
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<p><strong>Step 10:</strong>Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero.</p>
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<p><strong>Step 10:</strong>Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero.</p>
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<p>So the square root of √1029 is approximately 32.085.</p>
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<p>So the square root of √1029 is approximately 32.085.</p>
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<h2>Square Root of 1029 by Approximation Method</h2>
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<h2>Square Root of 1029 by Approximation Method</h2>
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<p>The approximation method is another method for finding the square roots; it is an easy method to find the square root of a given number. Now let us learn how to find the square root of 1029 using the approximation method.</p>
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<p>The approximation method is another method for finding the square roots; it is an easy method to find the square root of a given number. Now let us learn how to find the square root of 1029 using the approximation method.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect squares of √1029. The smallest perfect square<a>less than</a>1029 is 1024 (which is \(32^2\)), and the largest perfect square<a>greater than</a>1029 is 1089 (which is \(33^2\)). √1029 falls somewhere between 32 and 33.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect squares of √1029. The smallest perfect square<a>less than</a>1029 is 1024 (which is \(32^2\)), and the largest perfect square<a>greater than</a>1029 is 1089 (which is \(33^2\)). √1029 falls somewhere between 32 and 33.</p>
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<p><strong>Step 2:</strong>Now we need to apply the<a>formula</a>that is \((\text{Given number} - \text{smallest perfect square}) / (\text{Greater perfect square} - \text{smallest perfect square})\). Going by the formula \((1029 - 1024) / (1089 - 1024) = 5/65 = 0.077\). Using the formula, we identified the<a>decimal</a>point of our square root. The next step is adding the value we got initially to the decimal number, which is \(32 + 0.077 \approx 32.085\).</p>
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<p><strong>Step 2:</strong>Now we need to apply the<a>formula</a>that is \((\text{Given number} - \text{smallest perfect square}) / (\text{Greater perfect square} - \text{smallest perfect square})\). Going by the formula \((1029 - 1024) / (1089 - 1024) = 5/65 = 0.077\). Using the formula, we identified the<a>decimal</a>point of our square root. The next step is adding the value we got initially to the decimal number, which is \(32 + 0.077 \approx 32.085\).</p>
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<p>So the square root of 1029 is approximately 32.085.</p>
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<p>So the square root of 1029 is approximately 32.085.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 1029</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 1029</h2>
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<p>Students do make mistakes while finding the square root, like forgetting about the negative square root and skipping long division methods, etc. Now let us look at a few of those mistakes that students tend to make in detail.</p>
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<p>Students do make mistakes while finding the square root, like forgetting about the negative square root and skipping long division methods, etc. Now let us look at a few of those mistakes that students tend to make in detail.</p>
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<h2>Download Worksheets</h2>
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<h3>Problem 1</h3>
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<h3>Problem 1</h3>
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<p>Can you help Max find the area of a square box if its side length is given as √1029?</p>
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<p>Can you help Max find the area of a square box if its side length is given as √1029?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The area of the square is 1029 square units.</p>
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<p>The area of the square is 1029 square units.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>The area of the square = side².</p>
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<p>The area of the square = side².</p>
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<p>The side length is given as √1029.</p>
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<p>The side length is given as √1029.</p>
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<p>Area of the square = side²</p>
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<p>Area of the square = side²</p>
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<p>= √1029 × √1029</p>
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<p>= √1029 × √1029</p>
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<p>= 1029.</p>
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<p>= 1029.</p>
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<p>Therefore, the area of the square box is 1029 square units.</p>
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<p>Therefore, the area of the square box is 1029 square units.</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 2</h3>
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<h3>Problem 2</h3>
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<p>A square-shaped garden measuring 1029 square feet is planned; if each of the sides is √1029, what will be the square feet of half of the garden?</p>
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<p>A square-shaped garden measuring 1029 square feet is planned; if each of the sides is √1029, what will be the square feet of half of the garden?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>514.5 square feet</p>
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<p>514.5 square feet</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>We can just divide the given area by 2 as the garden is square-shaped.</p>
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<p>We can just divide the given area by 2 as the garden is square-shaped.</p>
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<p>Dividing 1029 by 2 = 514.5.</p>
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<p>Dividing 1029 by 2 = 514.5.</p>
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<p>So half of the garden measures 514.5 square feet.</p>
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<p>So half of the garden measures 514.5 square feet.</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 3</h3>
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<h3>Problem 3</h3>
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<p>Calculate √1029 × 5.</p>
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<p>Calculate √1029 × 5.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>160.425</p>
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<p>160.425</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>The first step is to find the square root of 1029, which is approximately 32.085.</p>
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<p>The first step is to find the square root of 1029, which is approximately 32.085.</p>
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<p>The second step is to multiply 32.085 with 5.</p>
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<p>The second step is to multiply 32.085 with 5.</p>
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<p>So 32.085 × 5 = 160.425.</p>
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<p>So 32.085 × 5 = 160.425.</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 4</h3>
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<h3>Problem 4</h3>
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<p>What will be the square root of (1000 + 29)?</p>
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<p>What will be the square root of (1000 + 29)?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The square root is approximately 32.085.</p>
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<p>The square root is approximately 32.085.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>To find the square root, we need to find the sum of (1000 + 29) = 1029.</p>
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<p>To find the square root, we need to find the sum of (1000 + 29) = 1029.</p>
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<p>The square root of 1029 is approximately 32.085.</p>
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<p>The square root of 1029 is approximately 32.085.</p>
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<p>Therefore, the square root of (1000 + 29) is approximately ±32.085.</p>
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<p>Therefore, the square root of (1000 + 29) is approximately ±32.085.</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 5</h3>
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<h3>Problem 5</h3>
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<p>Find the perimeter of the rectangle if its length ‘l’ is √1029 units and the width ‘w’ is 38 units.</p>
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<p>Find the perimeter of the rectangle if its length ‘l’ is √1029 units and the width ‘w’ is 38 units.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The perimeter of the rectangle is approximately 140.17 units.</p>
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<p>The perimeter of the rectangle is approximately 140.17 units.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Perimeter of the rectangle = 2 × (length + width).</p>
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<p>Perimeter of the rectangle = 2 × (length + width).</p>
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<p>Perimeter = 2 × (√1029 + 38)</p>
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<p>Perimeter = 2 × (√1029 + 38)</p>
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<p>= 2 × (32.085 + 38)</p>
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<p>= 2 × (32.085 + 38)</p>
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<p>= 2 × 70.085</p>
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<p>= 2 × 70.085</p>
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<p>= 140.17 units.</p>
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<p>= 140.17 units.</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h2>FAQ on Square Root of 1029</h2>
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<h2>FAQ on Square Root of 1029</h2>
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<h3>1.What is √1029 in its simplest form?</h3>
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<h3>1.What is √1029 in its simplest form?</h3>
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<p>The prime factorization of 1029 is 3 × 3 × 3 × 7 × 17, so the simplest form of √1029 = √(3 × 3 × 3 × 7 × 17).</p>
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<p>The prime factorization of 1029 is 3 × 3 × 3 × 7 × 17, so the simplest form of √1029 = √(3 × 3 × 3 × 7 × 17).</p>
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<h3>2.Mention the factors of 1029.</h3>
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<h3>2.Mention the factors of 1029.</h3>
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<p>Factors of 1029 are 1, 3, 7, 9, 17, 21, 27, 51, 63, 119, 153, 357, 513, and 1029.</p>
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<p>Factors of 1029 are 1, 3, 7, 9, 17, 21, 27, 51, 63, 119, 153, 357, 513, and 1029.</p>
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<h3>3.Calculate the square of 1029.</h3>
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<h3>3.Calculate the square of 1029.</h3>
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<p>We get the square of 1029 by multiplying the number by itself, that is 1029 × 1029 = 1,058,841.</p>
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<p>We get the square of 1029 by multiplying the number by itself, that is 1029 × 1029 = 1,058,841.</p>
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<h3>4.Is 1029 a prime number?</h3>
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<h3>4.Is 1029 a prime number?</h3>
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<p>1029 is not a<a>prime number</a>, as it has more than two factors.</p>
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<p>1029 is not a<a>prime number</a>, as it has more than two factors.</p>
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<h3>5.1029 is divisible by?</h3>
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<h3>5.1029 is divisible by?</h3>
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<p>1029 has many factors; those are 1, 3, 7, 9, 17, 21, 27, 51, 63, 119, 153, 357, 513, and 1029.</p>
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<p>1029 has many factors; those are 1, 3, 7, 9, 17, 21, 27, 51, 63, 119, 153, 357, 513, and 1029.</p>
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<h2>Important Glossaries for the Square Root of 1029</h2>
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<h2>Important Glossaries for the Square Root of 1029</h2>
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<ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: \(4^2 = 16\) and the inverse of the square is the square root, that is, √16 = 4. </li>
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<ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: \(4^2 = 16\) and the inverse of the square is the square root, that is, √16 = 4. </li>
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<li><strong>Irrational number:</strong>An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers. </li>
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<li><strong>Irrational number:</strong>An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers. </li>
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<li><strong>Principal square root:</strong>A number has both positive and negative square roots; however, it is always the positive square root that has more prominence due to its uses in the real world. That is the reason it is also known as the principal square root. </li>
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<li><strong>Principal square root:</strong>A number has both positive and negative square roots; however, it is always the positive square root that has more prominence due to its uses in the real world. That is the reason it is also known as the principal square root. </li>
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<li><strong>Long division method:</strong>A step-by-step approach to finding the square root of a number by dividing it into pairs of digits and solving iteratively. </li>
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<li><strong>Long division method:</strong>A step-by-step approach to finding the square root of a number by dividing it into pairs of digits and solving iteratively. </li>
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<li><strong>Approximation method:</strong>A technique used to estimate the square root of a number by finding nearby perfect squares and calculating the decimal portion based on their proximity.</li>
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<li><strong>Approximation method:</strong>A technique used to estimate the square root of a number by finding nearby perfect squares and calculating the decimal portion based on their proximity.</li>
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</ul><p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>
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</ul><p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>
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<p>▶</p>
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<p>▶</p>
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<h2>Jaskaran Singh Saluja</h2>
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<h2>Jaskaran Singh Saluja</h2>
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<h3>About the Author</h3>
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<h3>About the Author</h3>
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<p>Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.</p>
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<p>Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.</p>
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<h3>Fun Fact</h3>
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<h3>Fun Fact</h3>
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<p>: He loves to play the quiz with kids through algebra to make kids love it.</p>
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<p>: He loves to play the quiz with kids through algebra to make kids love it.</p>