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2026-01-01
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2026-02-28
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<p>235 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 and finance, among others. Here, we will discuss the square root of 7920.</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 and finance, among others. Here, we will discuss the square root of 7920.</p>
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<h2>What is the Square Root of 7920?</h2>
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<h2>What is the Square Root of 7920?</h2>
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<p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 7920 is not a<a>perfect square</a>. The square root of 7920 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √7920, whereas (7920)^(1/2) in the exponential form. √7920 ≈ 88.9833, 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>. 7920 is not a<a>perfect square</a>. The square root of 7920 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √7920, whereas (7920)^(1/2) in the exponential form. √7920 ≈ 88.9833, 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 7920</h2>
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<h2>Finding the Square Root of 7920</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 7920 by Prime Factorization Method</h2>
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</ul><h2>Square Root of 7920 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 7920 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 7920 is broken down into its prime factors.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 7920 Breaking it down, we get 2 x 2 x 2 x 2 x 3 x 3 x 5 x 11: 2^4 x 3^2 x 5 x 11</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 7920 Breaking it down, we get 2 x 2 x 2 x 2 x 3 x 3 x 5 x 11: 2^4 x 3^2 x 5 x 11</p>
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<p><strong>Step 2:</strong>Now we have found the prime factors of 7920. The second step is to make pairs of those prime factors. Since 7920 is not a perfect square, complete pairing is impossible. Therefore, calculating √7920 using prime factorization alone is not straightforward.</p>
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<p><strong>Step 2:</strong>Now we have found the prime factors of 7920. The second step is to make pairs of those prime factors. Since 7920 is not a perfect square, complete pairing is impossible. Therefore, calculating √7920 using prime factorization alone is not straightforward.</p>
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<h2>Square Root of 7920 by Long Division Method</h2>
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<h2>Square Root of 7920 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 7920, we need to group it as 20 and 79.</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 7920, we need to group it as 20 and 79.</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 79. We can say n as ‘8’ because 8 x 8 = 64 is less than or equal to 79. Now the<a>quotient</a>is 8, subtract 64 from 79, and the<a>remainder</a>is 15.</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 79. We can say n as ‘8’ because 8 x 8 = 64 is less than or equal to 79. Now the<a>quotient</a>is 8, subtract 64 from 79, and the<a>remainder</a>is 15.</p>
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<p><strong>Step 3:</strong>Now let us bring down 20, making the new<a>dividend</a>1520. Add the old<a>divisor</a>with the same number 8 + 8, giving us 16 as the new divisor</p>
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<p><strong>Step 3:</strong>Now let us bring down 20, making the new<a>dividend</a>1520. Add the old<a>divisor</a>with the same number 8 + 8, giving us 16 as the new divisor</p>
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<p><strong>Step 4:</strong>The new divisor will be the number formed by appending n to 16, making it 168. Now we need to find the value of n such that 168n x n is less than or equal to 1520.</p>
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<p><strong>Step 4:</strong>The new divisor will be the number formed by appending n to 16, making it 168. Now we need to find the value of n such that 168n x n is less than or equal to 1520.</p>
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<p><strong>Step 5:</strong>The next step is finding 168n x n ≤ 1520. Let us consider n as 9, now 168 x 9 = 1512, which is less than 1520.</p>
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<p><strong>Step 5:</strong>The next step is finding 168n x n ≤ 1520. Let us consider n as 9, now 168 x 9 = 1512, which is less than 1520.</p>
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<p><strong>Step 6:</strong>Subtract 1512 from 1520, the difference is 8, and the quotient is 89.</p>
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<p><strong>Step 6:</strong>Subtract 1512 from 1520, the difference is 8, and the quotient is 89.</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 800.</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 800.</p>
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<p><strong>Step 8:</strong>Continue this process until you achieve the desired level of accuracy. So the square root of √7920 is approximately 88.98.</p>
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<p><strong>Step 8:</strong>Continue this process until you achieve the desired level of accuracy. So the square root of √7920 is approximately 88.98.</p>
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<h2>Square Root of 7920 by Approximation Method</h2>
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<h2>Square Root of 7920 by Approximation Method</h2>
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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 7920 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 7920 using the approximation method.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √7920. The smallest perfect square below 7920 is 7840 (88^2) and the largest perfect square above 7920 is 8100 (90^2). √7920 falls somewhere between 88 and 90.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √7920. The smallest perfect square below 7920 is 7840 (88^2) and the largest perfect square above 7920 is 8100 (90^2). √7920 falls somewhere between 88 and 90.</p>
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<p><strong>Step 2:</strong>Now we need to apply the approximation<a>formula</a>: (Given number - smallest perfect square) ÷ (Greater perfect square - smallest perfect square). Using the formula (7920 - 7744) ÷ (8100 - 7744) = 176 ÷ 356 ≈ 0.4944 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 88 + 0.4944 ≈ 88.49.</p>
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<p><strong>Step 2:</strong>Now we need to apply the approximation<a>formula</a>: (Given number - smallest perfect square) ÷ (Greater perfect square - smallest perfect square). Using the formula (7920 - 7744) ÷ (8100 - 7744) = 176 ÷ 356 ≈ 0.4944 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 88 + 0.4944 ≈ 88.49.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 7920</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 7920</h2>
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<p>Students do make mistakes while finding the square root, like forgetting about the negative square root or skipping long division methods. 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 or skipping long division methods. 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 √7920?</p>
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<p>Can you help Max find the area of a square box if its side length is given as √7920?</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 7920 square units.</p>
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<p>The area of the square is 7920 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. The side length is given as √7920. Area of the square = side^2 = √7920 x √7920 = 7920. Therefore, the area of the square box is 7920 square units.</p>
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<p>The area of the square = side^2. The side length is given as √7920. Area of the square = side^2 = √7920 x √7920 = 7920. Therefore, the area of the square box is 7920 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 7920 square feet is built; if each of the sides is √7920, what will be the square feet of half of the building?</p>
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<p>A square-shaped building measuring 7920 square feet is built; if each of the sides is √7920, 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>3960 square feet</p>
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<p>3960 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. Dividing 7920 by 2 = 3960. So half of the building measures 3960 square feet.</p>
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<p>We can just divide the given area by 2 as the building is square-shaped. Dividing 7920 by 2 = 3960. So half of the building measures 3960 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 √7920 x 5.</p>
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<p>Calculate √7920 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>444.92</p>
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<p>444.92</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 7920, which is approximately 88.98. The second step is to multiply 88.98 with 5. So 88.98 x 5 = 444.92.</p>
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<p>The first step is to find the square root of 7920, which is approximately 88.98. The second step is to multiply 88.98 with 5. So 88.98 x 5 = 444.92.</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 (7920 + 80)?</p>
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<p>What will be the square root of (7920 + 80)?</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 90.11.</p>
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<p>The square root is approximately 90.11.</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 (7920 + 80). 7920 + 80 = 8000. The square root of 8000 is approximately 89.44. Therefore, the square root of (7920 + 80) is approximately 89.44.</p>
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<p>To find the square root, we need to find the sum of (7920 + 80). 7920 + 80 = 8000. The square root of 8000 is approximately 89.44. Therefore, the square root of (7920 + 80) is approximately 89.44.</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 √7920 units and the width ‘w’ is 40 units.</p>
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<p>Find the perimeter of the rectangle if its length ‘l’ is √7920 units and the width ‘w’ is 40 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 257.96 units.</p>
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<p>We find the perimeter of the rectangle as approximately 257.96 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 × (√7920 + 40) ≈ 2 × (88.98 + 40) ≈ 2 × 128.98 ≈ 257.96 units.</p>
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<p>Perimeter of the rectangle = 2 × (length + width). Perimeter = 2 × (√7920 + 40) ≈ 2 × (88.98 + 40) ≈ 2 × 128.98 ≈ 257.96 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 7920</h2>
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<h2>FAQ on Square Root of 7920</h2>
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<h3>1.What is √7920 in its simplest form?</h3>
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<h3>1.What is √7920 in its simplest form?</h3>
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<p>The prime factorization of 7920 is 2 x 2 x 2 x 2 x 3 x 3 x 5 x 11. Therefore, the simplest form of √7920 = √(2^4 x 3^2 x 5 x 11).</p>
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<p>The prime factorization of 7920 is 2 x 2 x 2 x 2 x 3 x 3 x 5 x 11. Therefore, the simplest form of √7920 = √(2^4 x 3^2 x 5 x 11).</p>
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<h3>2.Mention the factors of 7920.</h3>
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<h3>2.Mention the factors of 7920.</h3>
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<p>Factors of 7920 include 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 16, 20, 22, 24, 30, 33, 40, 44, 48, 55, 60, 66, 80, 88, 96, 110, 120, 132, 165, 176, 192, 220, 240, 264, 330, 352, 385, 440, 480, 528, 660, 704, 770, 880, 960, 1056, 1320, 1408, 1540, 1760, 2112, 2640, 3080, 3520, 4224, 5280, 6160, and 7920.</p>
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<p>Factors of 7920 include 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 16, 20, 22, 24, 30, 33, 40, 44, 48, 55, 60, 66, 80, 88, 96, 110, 120, 132, 165, 176, 192, 220, 240, 264, 330, 352, 385, 440, 480, 528, 660, 704, 770, 880, 960, 1056, 1320, 1408, 1540, 1760, 2112, 2640, 3080, 3520, 4224, 5280, 6160, and 7920.</p>
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<h3>3.Calculate the square of 7920.</h3>
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<h3>3.Calculate the square of 7920.</h3>
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<p>We get the square of 7920 by multiplying the number by itself, that is 7920 x 7920 = 62,726,400.</p>
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<p>We get the square of 7920 by multiplying the number by itself, that is 7920 x 7920 = 62,726,400.</p>
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<h3>4.Is 7920 a prime number?</h3>
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<h3>4.Is 7920 a prime number?</h3>
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<p>7920 is not a<a>prime number</a>, as it has more than two factors.</p>
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<p>7920 is not a<a>prime number</a>, as it has more than two factors.</p>
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<h3>5.7920 is divisible by?</h3>
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<h3>5.7920 is divisible by?</h3>
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<p>7920 has many factors; those include 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 16, 20, 22, 24, 30, 33, 40, 44, 48, 55, 60, 66, 80, 88, 96, 110, 120, 132, 165, 176, 192, 220, 240, 264, 330, 352, 385, 440, 480, 528, 660, 704, 770, 880, 960, 1056, 1320, 1408, 1540, 1760, 2112, 2640, 3080, 3520, 4224, 5280, 6160, and 7920.</p>
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<p>7920 has many factors; those include 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 16, 20, 22, 24, 30, 33, 40, 44, 48, 55, 60, 66, 80, 88, 96, 110, 120, 132, 165, 176, 192, 220, 240, 264, 330, 352, 385, 440, 480, 528, 660, 704, 770, 880, 960, 1056, 1320, 1408, 1540, 1760, 2112, 2640, 3080, 3520, 4224, 5280, 6160, and 7920.</p>
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<h2>Important Glossaries for the Square Root of 7920</h2>
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<h2>Important Glossaries for the Square Root of 7920</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>Approximation method:</strong>This method is used to estimate the square roots of non-perfect squares by identifying nearby perfect squares. </li>
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<li><strong>Approximation method:</strong>This method is used to estimate the square roots of non-perfect squares by identifying nearby perfect squares. </li>
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<li><strong>Long division method:</strong>A method used to find the square root of non-perfect squares through iterative division and subtraction. </li>
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<li><strong>Long division method:</strong>A method used to find the square root of non-perfect squares through iterative division and subtraction. </li>
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<li><strong>Prime factorization:</strong>The process of decomposing a number into its constituent prime numbers.</li>
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<li><strong>Prime factorization:</strong>The process of decomposing a number into its constituent prime numbers.</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>