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2026-01-01
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<p>186 Learners</p>
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<p>Last updated on<strong>September 30, 2025</strong></p>
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<p>Last updated on<strong>September 30, 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 616.</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 616.</p>
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<h2>What is the Square Root of 616?</h2>
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<h2>What is the Square Root of 616?</h2>
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<p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 616 is not a<a>perfect square</a>. The square root of 616 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √616, whereas (616)^(1/2) in the exponential form. √616 ≈ 24.8, 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>. 616 is not a<a>perfect square</a>. The square root of 616 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √616, whereas (616)^(1/2) in the exponential form. √616 ≈ 24.8, 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 616</h2>
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<h2>Finding the Square Root of 616</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>and approximation methods 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>and approximation methods 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 616 by Prime Factorization Method</h3>
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</ul><h3>Square Root of 616 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 616 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 616 is broken down into its prime factors.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 616 Breaking it down, we get 2 x 2 x 2 x 7 x 11: 2^3 x 7^1 x 11^1</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 616 Breaking it down, we get 2 x 2 x 2 x 7 x 11: 2^3 x 7^1 x 11^1</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 616. The second step is to make pairs of those prime factors. Since 616 is not a perfect square, therefore the digits of the number can’t be grouped in a pair. Therefore, calculating 616 using prime factorization is impossible.</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 616. The second step is to make pairs of those prime factors. Since 616 is not a perfect square, therefore the digits of the number can’t be grouped in a pair. Therefore, calculating 616 using prime factorization is impossible.</p>
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<h3>Square Root of 616 by Long Division Method</h3>
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<h3>Square Root of 616 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><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 616, we need to group it as 16 and 6.</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 616, we need to group it as 16 and 6.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is 6. We can say n as '2' because 2 x 2 is lesser than or equal to 6. Now the<a>quotient</a>is 2, and after subtracting 4 from 6, the<a>remainder</a>is 2.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is 6. We can say n as '2' because 2 x 2 is lesser than or equal to 6. Now the<a>quotient</a>is 2, and after subtracting 4 from 6, the<a>remainder</a>is 2.</p>
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<p><strong>Step 3:</strong>Now let us bring down 16, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 2 + 2 we get 4, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 16, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 2 + 2 we get 4, 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 4n 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 4n 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 4n x n ≤ 216; let us consider n as 5, now 45 x 5 = 225</p>
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<p><strong>Step 5:</strong>The next step is finding 4n x n ≤ 216; let us consider n as 5, now 45 x 5 = 225</p>
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<p><strong>Step 6:</strong>Subtract 225 from 216; the difference is 9, and the quotient is 24</p>
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<p><strong>Step 6:</strong>Subtract 225 from 216; the difference is 9, and the quotient is 24</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 900.</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 900.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 8 because 248 x 8 = 1984</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 8 because 248 x 8 = 1984</p>
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<p><strong>Step 9:</strong>Subtracting 1984 from 21600, we get the result 1600.</p>
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<p><strong>Step 9:</strong>Subtracting 1984 from 21600, we get the result 1600.</p>
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<p><strong>Step 10:</strong>Now the quotient is 24.8</p>
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<p><strong>Step 10:</strong>Now the quotient is 24.8</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 √616 is 24.8</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 √616 is 24.8</p>
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<h3>Square Root of 616 by Approximation Method</h3>
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<h3>Square Root of 616 by Approximation Method</h3>
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<p>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 616 using the approximation method.</p>
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<p>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 616 using the approximation method.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √616 The smallest perfect square of 616 is 576, and the largest perfect square of 616 is 625. √616 falls somewhere between 24 and 25.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √616 The smallest perfect square of 616 is 576, and the largest perfect square of 616 is 625. √616 falls somewhere between 24 and 25.</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). Going by the formula (616 - 576) ÷ (625 - 576) = 0.8 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 24 + 0.8 = 24.8, so the square root of 616 is 24.8.</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). Going by the formula (616 - 576) ÷ (625 - 576) = 0.8 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 24 + 0.8 = 24.8, so the square root of 616 is 24.8.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 616</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 616</h2>
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<p>Students do make mistakes while finding the square root, likewise 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, likewise 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 √616?</p>
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<p>Can you help Max find the area of a square box if its side length is given as √616?</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 616 square units.</p>
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<p>The area of the square is 616 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 √616.</p>
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<p>The side length is given as √616.</p>
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<p>Area of the square = side^2 = √616 x √616 = 24.8 × 24.8 = 616.</p>
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<p>Area of the square = side^2 = √616 x √616 = 24.8 × 24.8 = 616.</p>
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<p>Therefore, the area of the square box is 616 square units.</p>
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<p>Therefore, the area of the square box is 616 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 616 square feet is built; if each of the sides is √616, what will be the square feet of half of the building?</p>
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<p>A square-shaped building measuring 616 square feet is built; if each of the sides is √616, 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>308 square feet</p>
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<p>308 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 616 by 2, we get 308.</p>
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<p>Dividing 616 by 2, we get 308.</p>
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<p>So half of the building measures 308 square feet.</p>
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<p>So half of the building measures 308 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 √616 x 5.</p>
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<p>Calculate √616 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>124</p>
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<p>124</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 616, which is 24.8. The second step is to multiply 24.8 with 5. So 24.8 x 5 = 124.</p>
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<p>The first step is to find the square root of 616, which is 24.8. The second step is to multiply 24.8 with 5. So 24.8 x 5 = 124.</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 (576 + 40)?</p>
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<p>What will be the square root of (576 + 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 24.8</p>
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<p>The square root is 24.8</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 (576 + 40). 576 + 40 = 616, and then √616 = 24.8. Therefore, the square root of (576 + 40) is ±24.8.</p>
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<p>To find the square root, we need to find the sum of (576 + 40). 576 + 40 = 616, and then √616 = 24.8. Therefore, the square root of (576 + 40) is ±24.8.</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 √616 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 √616 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 125.6 units.</p>
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<p>We find the perimeter of the rectangle as 125.6 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 × (√616 + 38) = 2 × (24.8 + 38) = 2 × 62.8 = 125.6 units.</p>
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<p>Perimeter of the rectangle = 2 × (length + width). Perimeter = 2 × (√616 + 38) = 2 × (24.8 + 38) = 2 × 62.8 = 125.6 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 616</h2>
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<h2>FAQ on Square Root of 616</h2>
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<h3>1.What is √616 in its simplest form?</h3>
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<h3>1.What is √616 in its simplest form?</h3>
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<p>The prime factorization of 616 is 2 x 2 x 2 x 7 x 11, so the simplest form of √616 = √(2 x 2 x 2 x 7 x 11).</p>
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<p>The prime factorization of 616 is 2 x 2 x 2 x 7 x 11, so the simplest form of √616 = √(2 x 2 x 2 x 7 x 11).</p>
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<h3>2.Mention the factors of 616.</h3>
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<h3>2.Mention the factors of 616.</h3>
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<p>Factors of 616 are 1, 2, 4, 8, 11, 22, 28, 44, 56, 77, 88, 154, 308, and 616.</p>
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<p>Factors of 616 are 1, 2, 4, 8, 11, 22, 28, 44, 56, 77, 88, 154, 308, and 616.</p>
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<h3>3.Calculate the square of 616.</h3>
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<h3>3.Calculate the square of 616.</h3>
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<p>We get the square of 616 by multiplying the number by itself, that is, 616 x 616 = 379456.</p>
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<p>We get the square of 616 by multiplying the number by itself, that is, 616 x 616 = 379456.</p>
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<h3>4.Is 616 a prime number?</h3>
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<h3>4.Is 616 a prime number?</h3>
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<h3>5.616 is divisible by?</h3>
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<h3>5.616 is divisible by?</h3>
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<p>616 has many factors; those are 1, 2, 4, 8, 11, 22, 28, 44, 56, 77, 88, 154, 308, and 616.</p>
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<p>616 has many factors; those are 1, 2, 4, 8, 11, 22, 28, 44, 56, 77, 88, 154, 308, and 616.</p>
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<h2>Important Glossaries for the Square Root of 616</h2>
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<h2>Important Glossaries for the Square Root of 616</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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</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>Perfect square:</strong>A perfect square is a number that is the square of an integer. For example, 25 is a perfect square because it is 5^2.</li>
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</ul><ul><li><strong>Perfect square:</strong>A perfect square is a number that is the square of an integer. For example, 25 is a perfect square because it is 5^2.</li>
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</ul><ul><li><strong>Approximation:</strong>Approximation is the method of finding a number that is close to the exact value but not exact, used frequently in finding square roots of non-perfect squares.</li>
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</ul><ul><li><strong>Approximation:</strong>Approximation is the method of finding a number that is close to the exact value but not exact, used frequently in finding square roots of non-perfect squares.</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>