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2026-01-01
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2026-02-21
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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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 1496.</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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 1496.</p>
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<h2>What is the Square Root of 1496?</h2>
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<h2>What is the Square Root of 1496?</h2>
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<p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 1496 is not a<a>perfect square</a>. The square root of 1496 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √1496, whereas (1496)^(1/2) in exponential form. √1496 ≈ 38.6709, 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 of the square of the<a>number</a>. 1496 is not a<a>perfect square</a>. The square root of 1496 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √1496, whereas (1496)^(1/2) in exponential form. √1496 ≈ 38.6709, 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 1496</h2>
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<h2>Finding the Square Root of 1496</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 the 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 the 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 1496 by Prime Factorization Method</h2>
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</ul><h2>Square Root of 1496 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 1496 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 1496 is broken down into its prime factors:</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 1496 Breaking it down, we get 2 x 2 x 2 x 11 x 17: 2^3 x 11 x 17</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 1496 Breaking it down, we get 2 x 2 x 2 x 11 x 17: 2^3 x 11 x 17</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 1496. The second step is to make pairs of those prime factors. Since 1496 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 1496. The second step is to make pairs of those prime factors. Since 1496 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 1496 using prime factorization is impossible.</p>
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<p>Therefore, calculating 1496 using prime factorization is impossible.</p>
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<h2>Square Root of 1496 by Long Division Method</h2>
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<h2>Square Root of 1496 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 1496, we need to group it as 96 and 14.</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 1496, we need to group it as 96 and 14.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is<a>less than</a>or equal to 14. We can say n as ‘3’ because 3 x 3 = 9 is lesser than or equal to 14. Now the<a>quotient</a>is 3. After subtracting 9 from 14, the<a>remainder</a>is 5.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is<a>less than</a>or equal to 14. We can say n as ‘3’ because 3 x 3 = 9 is lesser than or equal to 14. Now the<a>quotient</a>is 3. After subtracting 9 from 14, the<a>remainder</a>is 5.</p>
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<p><strong>Step 3:</strong>Now let us bring down 96, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 3 + 3 to get 6, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 96, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 3 + 3 to get 6, which will be our new divisor.</p>
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<p><strong>Step 4:</strong>The new divisor will be the sum of the dividend and quotient. Now we get 6n as the new divisor, and we need to find the value of n.</p>
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<p><strong>Step 4:</strong>The new divisor will be the sum of the dividend and quotient. Now we get 6n as the new divisor, and we need to find the value of n.</p>
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<p><strong>Step 5:</strong>The next step is finding 6n × n ≤ 596. Let us consider n as 8, now 68 × 8 = 544.</p>
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<p><strong>Step 5:</strong>The next step is finding 6n × n ≤ 596. Let us consider n as 8, now 68 × 8 = 544.</p>
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<p><strong>Step 6:</strong>Subtract 596 from 544; the difference is 52, and the quotient is 38.</p>
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<p><strong>Step 6:</strong>Subtract 596 from 544; the difference is 52, and the quotient is 38.</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 5200.</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 5200.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor for which we add a digit to 76. Find a number such that when it multiplies with the number formed, it is less than or equal to 5200.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor for which we add a digit to 76. Find a number such that when it multiplies with the number formed, it is less than or equal to 5200.</p>
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<p><strong>Step 9:</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 9:</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 √1496 is approximately 38.6709.</p>
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<p>So the square root of √1496 is approximately 38.6709.</p>
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<h2>Square Root of 1496 by Approximation Method</h2>
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<h2>Square Root of 1496 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 1496 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 1496 using the approximation method.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √1496.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √1496.</p>
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<p>The smallest perfect square less than 1496 is 1444, and the largest perfect square<a>greater than</a>1496 is 1521. √1496 falls somewhere between 38 and 39.</p>
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<p>The smallest perfect square less than 1496 is 1444, and the largest perfect square<a>greater than</a>1496 is 1521. √1496 falls somewhere between 38 and 39.</p>
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<p><strong>Step 2:</strong>Now we need to apply the<a>formula</a>: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (1496 - 1444) ÷ (1521 - 1444) = 52 ÷ 77 ≈ 0.6753.</p>
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<p><strong>Step 2:</strong>Now we need to apply the<a>formula</a>: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (1496 - 1444) ÷ (1521 - 1444) = 52 ÷ 77 ≈ 0.6753.</p>
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<p>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 38 + 0.6753 ≈ 38.6753.</p>
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<p>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 38 + 0.6753 ≈ 38.6753.</p>
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<p>So the square root of 1496 is approximately 38.6753.</p>
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<p>So the square root of 1496 is approximately 38.6753.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 1496</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 1496</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 √1496?</p>
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<p>Can you help Max find the area of a square box if its side length is given as √1496?</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 1496 square units.</p>
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<p>The area of the square is 1496 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 √1496.</p>
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<p>The side length is given as √1496.</p>
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<p>Area of the square = side² = √1496 x √1496 = 1496.</p>
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<p>Area of the square = side² = √1496 x √1496 = 1496.</p>
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<p>Therefore, the area of the square box is 1496 square units.</p>
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<p>Therefore, the area of the square box is 1496 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 building measuring 1496 square feet is built; if each of the sides is √1496, what will be the square feet of half of the building?</p>
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<p>A square-shaped building measuring 1496 square feet is built; if each of the sides is √1496, what will be the square feet of half of the building?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>748 square feet</p>
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<p>748 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 building is square-shaped.</p>
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<p>We can just divide the given area by 2 as the building is square-shaped.</p>
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<p>Dividing 1496 by 2 = we get 748.</p>
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<p>Dividing 1496 by 2 = we get 748.</p>
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<p>So half of the building measures 748 square feet.</p>
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<p>So half of the building measures 748 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 √1496 x 5.</p>
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<p>Calculate √1496 x 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>193.3545</p>
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<p>193.3545</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 1496, which is approximately 38.6709.</p>
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<p>The first step is to find the square root of 1496, which is approximately 38.6709.</p>
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<p>The second step is to multiply 38.6709 by 5.</p>
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<p>The second step is to multiply 38.6709 by 5.</p>
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<p>So 38.6709 x 5 ≈ 193.3545.</p>
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<p>So 38.6709 x 5 ≈ 193.3545.</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 (1456 + 40)?</p>
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<p>What will be the square root of (1456 + 40)?</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 40.</p>
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<p>The square root is 40.</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 (1456 + 40). 1456 + 40 = 1496, and then √1496 ≈ 38.6709.</p>
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<p>To find the square root, we need to find the sum of (1456 + 40). 1456 + 40 = 1496, and then √1496 ≈ 38.6709.</p>
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<p>Therefore, the square root of (1456 + 40) is approximately ±38.6709.</p>
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<p>Therefore, the square root of (1456 + 40) is approximately ±38.6709.</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 √1496 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 √1496 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>We find the perimeter of the rectangle as approximately 153.3418 units.</p>
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<p>We find the perimeter of the rectangle as approximately 153.3418 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 × (√1496 + 38) = 2 × (38.6709 + 38) ≈ 2 × 76.6709 ≈ 153.3418 units.</p>
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<p>Perimeter = 2 × (√1496 + 38) = 2 × (38.6709 + 38) ≈ 2 × 76.6709 ≈ 153.3418 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 1496</h2>
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<h2>FAQ on Square Root of 1496</h2>
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<h3>1.What is √1496 in its simplest form?</h3>
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<h3>1.What is √1496 in its simplest form?</h3>
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<p>The prime factorization of 1496 is 2 x 2 x 2 x 11 x 17, so the simplest form of √1496 = √(2 x 2 x 2 x 11 x 17).</p>
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<p>The prime factorization of 1496 is 2 x 2 x 2 x 11 x 17, so the simplest form of √1496 = √(2 x 2 x 2 x 11 x 17).</p>
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<h3>2.Mention the factors of 1496.</h3>
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<h3>2.Mention the factors of 1496.</h3>
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<p>Factors of 1496 are 1, 2, 4, 8, 11, 17, 22, 34, 44, 68, 88, 136, 187, 272, 374, 748, and 1496.</p>
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<p>Factors of 1496 are 1, 2, 4, 8, 11, 17, 22, 34, 44, 68, 88, 136, 187, 272, 374, 748, and 1496.</p>
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<h3>3.Calculate the square of 1496.</h3>
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<h3>3.Calculate the square of 1496.</h3>
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<p>We get the square of 1496 by multiplying the number by itself, that is 1496 x 1496 = 2,238,016.</p>
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<p>We get the square of 1496 by multiplying the number by itself, that is 1496 x 1496 = 2,238,016.</p>
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<h3>4.Is 1496 a prime number?</h3>
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<h3>4.Is 1496 a prime number?</h3>
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<p>1496 is not a<a>prime number</a>, as it has more than two factors.</p>
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<p>1496 is not a<a>prime number</a>, as it has more than two factors.</p>
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<h3>5.1496 is divisible by?</h3>
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<h3>5.1496 is divisible by?</h3>
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<p>1496 has many factors; those are 1, 2, 4, 8, 11, 17, 22, 34, 44, 68, 88, 136, 187, 272, 374, 748, and 1496.</p>
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<p>1496 has many factors; those are 1, 2, 4, 8, 11, 17, 22, 34, 44, 68, 88, 136, 187, 272, 374, 748, and 1496.</p>
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<h2>Important Glossaries for the Square Root of 1496</h2>
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<h2>Important Glossaries for the Square Root of 1496</h2>
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<ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: 4² = 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: 4² = 16, and the inverse of the square is the square root, that is, √16 = 4.</li>
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</ul><ul><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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</ul><ul><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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</ul><ul><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 a principal square root.</li>
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</ul><ul><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 a principal square root.</li>
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</ul><ul><li><strong>Approximation method:</strong>A method used to find the square root of non-perfect squares by finding the nearest perfect squares and calculating a decimal approximation.</li>
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</ul><ul><li><strong>Approximation method:</strong>A method used to find the square root of non-perfect squares by finding the nearest perfect squares and calculating a decimal approximation.</li>
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</ul><ul><li><strong>Long division method:</strong>A step-by-step method used to find the square root of non-perfect square numbers through repeated division and subtraction.</li>
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</ul><ul><li><strong>Long division method:</strong>A step-by-step method used to find the square root of non-perfect square numbers through repeated division and subtraction.</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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<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>