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2026-01-01
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2026-02-28
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<p>261 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 architecture, finance, and engineering. Here, we will discuss the square root of 60.</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 architecture, finance, and engineering. Here, we will discuss the square root of 60.</p>
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<h2>What is the Square Root of 60?</h2>
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<h2>What is the Square Root of 60?</h2>
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<p>The<a>square</a>root is the inverse of the square of a<a>number</a>. 60 is not a<a>perfect square</a>. The square root of 60 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √60, whereas (60)^(1/2) in the exponential form. √60 ≈ 7.74597, 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 a<a>number</a>. 60 is not a<a>perfect square</a>. The square root of 60 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √60, whereas (60)^(1/2) in the exponential form. √60 ≈ 7.74597, 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 60</h2>
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<h2>Finding the Square Root of 60</h2>
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<p>The<a>prime factorization</a>method is used for perfect square numbers. However, for non-perfect square numbers, methods like the long-<a>division</a>method and approximation method are used. Let us now learn the following methods: - Prime factorization method</p>
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<p>The<a>prime factorization</a>method is used for perfect square numbers. However, for non-perfect square numbers, methods like the long-<a>division</a>method and approximation method are used. Let us now learn the following methods: - Prime factorization method</p>
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<ul><li>Long division method</li>
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<ul><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 60 by Prime Factorization Method</h3>
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</ul><h3>Square Root of 60 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 60 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 60 is broken down into its prime factors.</p>
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<p>Step 1: Finding the prime factors of 60</p>
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<p>Step 1: Finding the prime factors of 60</p>
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<p>Breaking it down, we get 2 x 2 x 3 x 5: 2^2 x 3^1 x 5^1</p>
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<p>Breaking it down, we get 2 x 2 x 3 x 5: 2^2 x 3^1 x 5^1</p>
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<p>Step 2: Now we found out the prime factors of 60. The second step is to make pairs of those prime factors. Since 60 is not a perfect square, the digits of the number can’t be grouped in pairs.</p>
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<p>Step 2: Now we found out the prime factors of 60. The second step is to make pairs of those prime factors. Since 60 is not a perfect square, the digits of the number can’t be grouped in pairs.</p>
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<p>Therefore, calculating √60 using prime factorization gives us 2√15, which is an irrational number.</p>
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<p>Therefore, calculating √60 using prime factorization gives us 2√15, which is an irrational number.</p>
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<h2>Square Root of 60 by Long Division Method</h2>
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<h2>Square Root of 60 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 60, we need to group it as 60.</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 60, we need to group it as 60.</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 60. We can say n as ‘7’ because 7 x 7 = 49, which is less than 60. Now the<a>quotient</a>is 7, and the<a>remainder</a>is 60 - 49 = 11.</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 60. We can say n as ‘7’ because 7 x 7 = 49, which is less than 60. Now the<a>quotient</a>is 7, and the<a>remainder</a>is 60 - 49 = 11.</p>
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<p><strong>Step 3:</strong>Now let us bring down 00, which makes the new<a>dividend</a>1100.</p>
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<p><strong>Step 3:</strong>Now let us bring down 00, which makes the new<a>dividend</a>1100.</p>
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<p><strong>Step 4:</strong>Double the<a>divisor</a>(7) and write it as 14.</p>
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<p><strong>Step 4:</strong>Double the<a>divisor</a>(7) and write it as 14.</p>
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<p><strong>Step 5:</strong>We need to find a digit x such that 14x x x ≤ 1100. Trying x = 7 gives us 1447 x 7 = 10129, which is too large. Trying x = 6 gives us 146 x 6 = 876, which fits.</p>
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<p><strong>Step 5:</strong>We need to find a digit x such that 14x x x ≤ 1100. Trying x = 7 gives us 1447 x 7 = 10129, which is too large. Trying x = 6 gives us 146 x 6 = 876, which fits.</p>
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<p><strong>Step 6:</strong>Subtract 876 from 1100, which gives 224.</p>
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<p><strong>Step 6:</strong>Subtract 876 from 1100, which gives 224.</p>
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<p><strong>Step 7:</strong>Since the remainder is not zero, continue the process with the new dividend 22400 and new divisor 1460.</p>
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<p><strong>Step 7:</strong>Since the remainder is not zero, continue the process with the new dividend 22400 and new divisor 1460.</p>
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<p><strong>Step 8:</strong>The next x is found similarly. After a few more steps, we calculate the square root of 60 as approximately 7.74.</p>
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<p><strong>Step 8:</strong>The next x is found similarly. After a few more steps, we calculate the square root of 60 as approximately 7.74.</p>
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<h2>Square Root of 60 by Approximation Method</h2>
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<h2>Square Root of 60 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 60 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 60 using the approximation method.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect squares of 60. The smallest perfect square less than 60 is 49 (7^2), and the largest perfect square<a>greater than</a>60 is 64 (8^2). √60 falls somewhere between 7 and 8.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect squares of 60. The smallest perfect square less than 60 is 49 (7^2), and the largest perfect square<a>greater than</a>60 is 64 (8^2). √60 falls somewhere between 7 and 8.</p>
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<p><strong>Step 2:</strong>Now we need to apply the<a>formula</a>: (Given number - smaller perfect square) / (Greater perfect square - smaller perfect square). Going by the formula (60 - 49) / (64 - 49) = 11/15 ≈ 0.733</p>
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<p><strong>Step 2:</strong>Now we need to apply the<a>formula</a>: (Given number - smaller perfect square) / (Greater perfect square - smaller perfect square). Going by the formula (60 - 49) / (64 - 49) = 11/15 ≈ 0.733</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 7 + 0.733 = 7.733, so the square root of 60 is approximately 7.73.</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 7 + 0.733 = 7.733, so the square root of 60 is approximately 7.73.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 60</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 60</h2>
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<p>Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in long division. Now let us look at a few of those mistakes that students tend to make in detail.</p>
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<p>Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in long division. 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 √60?</p>
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<p>Can you help Max find the area of a square box if its side length is given as √60?</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 60 square units.</p>
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<p>The area of the square is approximately 60 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 √60.</p>
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<p>The side length is given as √60.</p>
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<p>Area of the square = (√60)² = 60.</p>
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<p>Area of the square = (√60)² = 60.</p>
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<p>Therefore, the area of the square box is approximately 60 square units.</p>
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<p>Therefore, the area of the square box is approximately 60 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 60 square feet is built; if each of the sides is √60, what will be the square feet of half of the building?</p>
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<p>A square-shaped building measuring 60 square feet is built; if each of the sides is √60, 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>30 square feet</p>
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<p>30 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 60 by 2, we get 30.</p>
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<p>Dividing 60 by 2, we get 30.</p>
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<p>So half of the building measures 30 square feet.</p>
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<p>So half of the building measures 30 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 √60 × 5.</p>
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<p>Calculate √60 × 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>Approximately 38.73</p>
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<p>Approximately 38.73</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 60, which is approximately 7.74597.</p>
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<p>The first step is to find the square root of 60, which is approximately 7.74597.</p>
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<p>The second step is to multiply 7.74597 by 5.</p>
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<p>The second step is to multiply 7.74597 by 5.</p>
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<p>So 7.74597 × 5 ≈ 38.73.</p>
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<p>So 7.74597 × 5 ≈ 38.73.</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 (56 + 4)?</p>
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<p>What will be the square root of (56 + 4)?</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 8.</p>
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<p>The square root is 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 (56 + 4). 56 + 4 = 60, and then √60 = approximately ±7.74597.</p>
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<p>To find the square root, we need to find the sum of (56 + 4). 56 + 4 = 60, and then √60 = approximately ±7.74597.</p>
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<p>Therefore, the square root of (56 + 4) is approximately 7.74597.</p>
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<p>Therefore, the square root of (56 + 4) is approximately 7.74597.</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 √60 units and the width ‘w’ is 20 units.</p>
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<p>Find the perimeter of the rectangle if its length ‘l’ is √60 units and the width ‘w’ is 20 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 55.49 units.</p>
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<p>The perimeter of the rectangle is approximately 55.49 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 × (√60 + 20) ≈ 2 × (7.74597 + 20) ≈ 2 × 27.74597 ≈ 55.49 units.</p>
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<p>Perimeter = 2 × (√60 + 20) ≈ 2 × (7.74597 + 20) ≈ 2 × 27.74597 ≈ 55.49 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 60</h2>
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<h2>FAQ on Square Root of 60</h2>
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<h3>1.What is √60 in its simplest form?</h3>
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<h3>1.What is √60 in its simplest form?</h3>
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<p>The prime factorization of 60 is 2 × 2 × 3 × 5, so the simplest form of √60 = √(2 × 2 × 3 × 5) = 2√15.</p>
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<p>The prime factorization of 60 is 2 × 2 × 3 × 5, so the simplest form of √60 = √(2 × 2 × 3 × 5) = 2√15.</p>
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<h3>2.Mention the factors of 60.</h3>
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<h3>2.Mention the factors of 60.</h3>
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<p>Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.</p>
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<p>Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.</p>
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<h3>3.Calculate the square of 60.</h3>
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<h3>3.Calculate the square of 60.</h3>
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<p>We get the square of 60 by multiplying the number by itself, that is 60 × 60 = 3600.</p>
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<p>We get the square of 60 by multiplying the number by itself, that is 60 × 60 = 3600.</p>
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<h3>4.Is 60 a prime number?</h3>
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<h3>4.Is 60 a prime number?</h3>
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<h3>5.60 is divisible by?</h3>
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<h3>5.60 is divisible by?</h3>
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<p>60 has many factors; those are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.</p>
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<p>60 has many factors; those are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.</p>
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<h2>Important Glossaries for the Square Root of 60</h2>
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<h2>Important Glossaries for the Square Root of 60</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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<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:</strong>The process of finding a value that is close to the actual value, often used for non-perfect squares. </li>
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<li><strong>Approximation:</strong>The process of finding a value that is close to the actual value, often used for non-perfect squares. </li>
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<li><strong>Prime factorization:</strong>Breaking down a number into its basic prime number components. </li>
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<li><strong>Prime factorization:</strong>Breaking down a number into its basic prime number components. </li>
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<li><strong>Long division method:</strong>A systematic approach for finding the square root of non-perfect squares by using division.</li>
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<li><strong>Long division method:</strong>A systematic approach for finding the square root of non-perfect squares by using division.</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>