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2026-01-01
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2026-02-28
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<p>219 Learners</p>
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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 fields such as vehicle design, finance, etc. Here, we will discuss the square root of 1140.</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 fields such as vehicle design, finance, etc. Here, we will discuss the square root of 1140.</p>
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<h2>What is the Square Root of 1140?</h2>
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<h2>What is the Square Root of 1140?</h2>
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<p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 1140 is not a<a>perfect square</a>. The square root of 1140 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √1140, whereas (1140)^(1/2) in the exponential form. √1140 ≈ 33.7406, 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>. 1140 is not a<a>perfect square</a>. The square root of 1140 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √1140, whereas (1140)^(1/2) in the exponential form. √1140 ≈ 33.7406, 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 1140</h2>
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<h2>Finding the Square Root of 1140</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><h3>Square Root of 1140 by Prime Factorization Method</h3>
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</ul><h3>Square Root of 1140 by Prime Factorization Method</h3>
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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 1140 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 1140 is broken down into its prime factors:</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 1140 Breaking it down, we get 2 × 2 × 3 × 5 × 19: 2^2 × 3^1 × 5^1 × 19^1</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 1140 Breaking it down, we get 2 × 2 × 3 × 5 × 19: 2^2 × 3^1 × 5^1 × 19^1</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 1140. The second step is to make pairs of those prime factors. Since 1140 is not a perfect square, therefore the digits of the number can’t be grouped in pairs. Therefore, calculating 1140 using prime factorization is impossible.</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 1140. The second step is to make pairs of those prime factors. Since 1140 is not a perfect square, therefore the digits of the number can’t be grouped in pairs. Therefore, calculating 1140 using prime factorization is impossible.</p>
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<h3>Square Root of 1140 by Long Division Method</h3>
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<h3>Square Root of 1140 by Long Division Method</h3>
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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>Step 1: To begin with, we need to group the numbers from right to left. In the case of 1140, we need to group it as 40 and 11.</p>
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<p>Step 1: To begin with, we need to group the numbers from right to left. In the case of 1140, we need to group it as 40 and 11.</p>
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<p>Step 2: Now we need to find n whose square is 11. We can say n is ‘3’ because 3 × 3 is<a>less than</a>or equal to 11. Now the<a>quotient</a>is 3 and after subtracting 9 from 11 the<a>remainder</a>is 2.</p>
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<p>Step 2: Now we need to find n whose square is 11. We can say n is ‘3’ because 3 × 3 is<a>less than</a>or equal to 11. Now the<a>quotient</a>is 3 and after subtracting 9 from 11 the<a>remainder</a>is 2.</p>
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<p>Step 3: Now let us bring down 40 which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 3 + 3 we get 6 which will be our new divisor.</p>
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<p>Step 3: Now let us bring down 40 which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 3 + 3 we get 6 which will be our new divisor.</p>
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<p>Step 4: The new divisor will be the sum 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>Step 4: The new divisor will be the sum 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>Step 5: The next step is finding 6n × n ≤ 240. Let us consider n as 3, now 6 × 3 × 3 = 54.</p>
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<p>Step 5: The next step is finding 6n × n ≤ 240. Let us consider n as 3, now 6 × 3 × 3 = 54.</p>
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<p><strong>Step 6:</strong>Subtract 54 from 240, the difference is 186, and the quotient is 33.</p>
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<p><strong>Step 6:</strong>Subtract 54 from 240, the difference is 186, and the quotient is 33.</p>
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<p><strong>Step 7:</strong>Since the dividend is larger than the divisor, we need to continue the process. Adding a decimal point allows us to add two zeroes to the dividend. Now the new dividend is 18600.</p>
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<p><strong>Step 7:</strong>Since the dividend is larger than the divisor, we need to continue the process. Adding a decimal point allows us to add two zeroes to the dividend. Now the new dividend is 18600.</p>
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<p><strong>Step 8</strong>: Now we need to find the new divisor that is 678 because 678 × 2 = 1356. Step 9: Subtracting 1356 from 18600 we get the result 5044.</p>
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<p><strong>Step 8</strong>: Now we need to find the new divisor that is 678 because 678 × 2 = 1356. Step 9: Subtracting 1356 from 18600 we get the result 5044.</p>
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<p><strong>Step 10:</strong>Now the quotient is 33.7.</p>
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<p><strong>Step 10:</strong>Now the quotient is 33.7.</p>
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<p><strong>Step 11:</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. So, the square root of √1140 ≈ 33.74.</p>
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<p><strong>Step 11:</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. So, the square root of √1140 ≈ 33.74.</p>
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<h3>Square Root of 1140 by Approximation Method</h3>
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<h3>Square Root of 1140 by Approximation Method</h3>
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<p>The approximation method is another method for finding 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 1140 using the approximation method.</p>
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<p>The approximation method is another method for finding 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 1140 using the approximation method.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √1140. The smallest perfect square less than 1140 is 1089 and the largest perfect square<a>greater than</a>1140 is 1156. √1140 falls somewhere between 33 and 34.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √1140. The smallest perfect square less than 1140 is 1089 and the largest perfect square<a>greater than</a>1140 is 1156. √1140 falls somewhere between 33 and 34.</p>
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<p><strong>Step 2:</strong>Now we need to apply the<a>formula</a>that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (1140 - 1089) / (1156 - 1089) = 51 / 67 ≈ 0.76. 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 33 + 0.76 = 33.76, so the square root of 1140 is approximately 33.76.</p>
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<p><strong>Step 2:</strong>Now we need to apply the<a>formula</a>that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (1140 - 1089) / (1156 - 1089) = 51 / 67 ≈ 0.76. 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 33 + 0.76 = 33.76, so the square root of 1140 is approximately 33.76.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 1140</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 1140</h2>
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<p>Students do make mistakes while finding the square root, such as forgetting about the negative square root, 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, such as forgetting about the negative square root, 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 √1140?</p>
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<p>Can you help Max find the area of a square box if its side length is given as √1140?</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 approximately 1140 square units.</p>
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<p>The area of the square is approximately 1140 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 = side^2.</p>
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<p>The area of the square = side^2.</p>
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<p>The side length is given as √1140.</p>
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<p>The side length is given as √1140.</p>
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<p>Area of the square = side^2 = √1140 × √1140 = 1140.</p>
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<p>Area of the square = side^2 = √1140 × √1140 = 1140.</p>
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<p>Therefore, the area of the square box is approximately 1140 square units.</p>
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<p>Therefore, the area of the square box is approximately 1140 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 1140 square feet is built; if each of the sides is √1140, what will be the square feet of half of the building?</p>
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<p>A square-shaped building measuring 1140 square feet is built; if each of the sides is √1140, 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>570 square feet</p>
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<p>570 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 1140 by 2 = we get 570.</p>
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<p>Dividing 1140 by 2 = we get 570.</p>
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<p>So, half of the building measures 570 square feet.</p>
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<p>So, half of the building measures 570 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 √1140 × 5.</p>
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<p>Calculate √1140 × 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>168.703</p>
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<p>168.703</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 1140 which is approximately 33.7406, the second step is to multiply 33.7406 by 5. So, 33.7406 × 5 ≈ 168.703.</p>
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<p>The first step is to find the square root of 1140 which is approximately 33.7406, the second step is to multiply 33.7406 by 5. So, 33.7406 × 5 ≈ 168.703.</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 (1140 + 16)?</p>
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<p>What will be the square root of (1140 + 16)?</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 34.</p>
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<p>The square root is approximately 34.</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 (1140 + 16). 1140 + 16 = 1156, and then √1156 = 34. Therefore, the square root of (1140 + 16) is ±34.</p>
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<p>To find the square root, we need to find the sum of (1140 + 16). 1140 + 16 = 1156, and then √1156 = 34. Therefore, the square root of (1140 + 16) is ±34.</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 √1140 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 √1140 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 143.48 units.</p>
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<p>The perimeter of the rectangle is approximately 143.48 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). Perimeter = 2 × (√1140 + 38) = 2 × (33.7406 + 38) = 2 × 71.7406 ≈ 143.48 units.</p>
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<p>Perimeter of the rectangle = 2 × (length + width). Perimeter = 2 × (√1140 + 38) = 2 × (33.7406 + 38) = 2 × 71.7406 ≈ 143.48 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 1140</h2>
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<h2>FAQ on Square Root of 1140</h2>
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<h3>1.What is √1140 in its simplest form?</h3>
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<h3>1.What is √1140 in its simplest form?</h3>
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<p>The prime factorization of 1140 is 2 × 2 × 3 × 5 × 19, so the simplest form of √1140 = √(2 × 2 × 3 × 5 × 19).</p>
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<p>The prime factorization of 1140 is 2 × 2 × 3 × 5 × 19, so the simplest form of √1140 = √(2 × 2 × 3 × 5 × 19).</p>
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<h3>2.Mention the factors of 1140.</h3>
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<h3>2.Mention the factors of 1140.</h3>
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<p>Factors of 1140 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 19, 20, 30, 38, 57, 60, 76, 95, 114, 190, 228, 285, 380, 570, and 1140.</p>
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<p>Factors of 1140 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 19, 20, 30, 38, 57, 60, 76, 95, 114, 190, 228, 285, 380, 570, and 1140.</p>
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<h3>3.Calculate the square of 1140.</h3>
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<h3>3.Calculate the square of 1140.</h3>
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<p>We get the square of 1140 by multiplying the number by itself, that is 1140 × 1140 = 1,299,600.</p>
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<p>We get the square of 1140 by multiplying the number by itself, that is 1140 × 1140 = 1,299,600.</p>
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<h3>4.Is 1140 a prime number?</h3>
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<h3>4.Is 1140 a prime number?</h3>
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<p>1140 is not a<a>prime number</a>, as it has more than two factors.</p>
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<p>1140 is not a<a>prime number</a>, as it has more than two factors.</p>
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<h3>5.1140 is divisible by?</h3>
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<h3>5.1140 is divisible by?</h3>
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<p>1140 is divisible by 1, 2, 3, 4, 5, 6, 10, 12, 15, 19, 20, 30, 38, 57, 60, 76, 95, 114, 190, 228, 285, 380, 570, and 1140.</p>
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<p>1140 is divisible by 1, 2, 3, 4, 5, 6, 10, 12, 15, 19, 20, 30, 38, 57, 60, 76, 95, 114, 190, 228, 285, 380, 570, and 1140.</p>
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<h2>Important Glossaries for the Square Root of 1140</h2>
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<h2>Important Glossaries for the Square Root of 1140</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.<strong></strong></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.<strong></strong></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 the 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 the principal square root.</li>
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</ul><ul><li><strong>Prime factorization:</strong>The process of decomposing a number into its prime factors. For example, the prime factorization of 1140 is 2 × 2 × 3 × 5 × 19.</li>
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</ul><ul><li><strong>Prime factorization:</strong>The process of decomposing a number into its prime factors. For example, the prime factorization of 1140 is 2 × 2 × 3 × 5 × 19.</li>
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</ul><ul><li><strong>Long division method:</strong>A technique used to find the square root of non-perfect squares by breaking down the number into smaller, more manageable parts through a series of division steps.</li>
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</ul><ul><li><strong>Long division method:</strong>A technique used to find the square root of non-perfect squares by breaking down the number into smaller, more manageable parts through a series of division steps.</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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<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>