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2026-01-01
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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 various fields such as vehicle design and finance. Here, we will discuss the square root of 960.</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 various fields such as vehicle design and finance. Here, we will discuss the square root of 960.</p>
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<h2>What is the Square Root of 960?</h2>
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<h2>What is the Square Root of 960?</h2>
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<p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 960 is not a<a>perfect square</a>. The square root of 960 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √960, whereas (960)(1/2) in the exponential form. √960 = 30.98387, 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>. 960 is not a<a>perfect square</a>. The square root of 960 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √960, whereas (960)(1/2) in the exponential form. √960 = 30.98387, 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 960</h2>
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<h2>Finding the Square Root of 960</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>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 long-<a>division</a>method and approximation method are used. Let us now learn the following methods:</p>
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<ol><li>Prime factorization method</li>
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<ol><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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</ol><h2>Square Root of 960 by Prime Factorization Method</h2>
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</ol><h2>Square Root of 960 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 960 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 960 is broken down into its prime factors.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 960 Breaking it down, we get 2 x 2 x 2 x 2 x 2 x 3 x 5:<a>2^5</a>x 3 x 5</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 960 Breaking it down, we get 2 x 2 x 2 x 2 x 2 x 3 x 5:<a>2^5</a>x 3 x 5</p>
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<p><strong>Step 2:</strong>Now we found the prime factors of 960. The second step is to make pairs of those prime factors. Since 960 is not a perfect square, the digits of the number can’t be grouped in pairs that result in a perfect square.</p>
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<p><strong>Step 2:</strong>Now we found the prime factors of 960. The second step is to make pairs of those prime factors. Since 960 is not a perfect square, the digits of the number can’t be grouped in pairs that result in a perfect square.</p>
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<p>Therefore, calculating 960 using prime factorization does not yield an exact integer.</p>
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<p>Therefore, calculating 960 using prime factorization does not yield an exact integer.</p>
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<h2>Square Root of 960 by Long Division Method</h2>
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<h2>Square Root of 960 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 960, we need to group it as 60 and 9.</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 960, we need to group it as 60 and 9.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is 9. We can say n as ‘3’ because 3 x 3 is equal to 9. Now the<a>quotient</a>is 3 after subtracting 9-9 the<a>remainder</a>is 0.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is 9. We can say n as ‘3’ because 3 x 3 is equal to 9. Now the<a>quotient</a>is 3 after subtracting 9-9 the<a>remainder</a>is 0.</p>
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<p><strong>Step 3:</strong>Now let us bring down 60, 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><strong>Step 3:</strong>Now let us bring down 60, 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><strong>Step 4:</strong>The new divisor will be the<a>sum</a>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><strong>Step 4:</strong>The new divisor will be the<a>sum</a>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><strong>Step 5:</strong>The next step is finding 6n x n ≤ 60; let us consider n as 0, now 6 x 0 x 0 = 0</p>
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<p><strong>Step 5:</strong>The next step is finding 6n x n ≤ 60; let us consider n as 0, now 6 x 0 x 0 = 0</p>
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<p><strong>Step 6:</strong>Subtract 60 from 0, the difference is 60, and the quotient is 30.</p>
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<p><strong>Step 6:</strong>Subtract 60 from 0, the difference is 60, and the quotient is 30.</p>
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<p><strong>Step 7:</strong>Since the dividend is greater than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeros to the dividend. Now the new dividend is 6000.</p>
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<p><strong>Step 7:</strong>Since the dividend is greater than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeros to the dividend. Now the new dividend is 6000.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 309 because 309 x 9 = 2781</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 309 because 309 x 9 = 2781</p>
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<p><strong>Step 9:</strong>Subtracting 2781 from 6000, we get the result 3219.</p>
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<p><strong>Step 9:</strong>Subtracting 2781 from 6000, we get the result 3219.</p>
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<p><strong>Step 10:</strong>Now the quotient is 30.9</p>
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<p><strong>Step 10:</strong>Now the quotient is 30.9</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 is no decimal values continue till the remainder is zero So the square root of √960 is approximately 30.98.</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 is no decimal values continue till the remainder is zero So the square root of √960 is approximately 30.98.</p>
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<h2>Square Root of 960 by Approximation Method</h2>
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<h2>Square Root of 960 by Approximation Method</h2>
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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 960 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 960 using the approximation method.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √960. The smallest perfect square below 960 is 961, and the largest perfect square below 960 is 900. √960 falls somewhere between 30 and 31.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √960. The smallest perfect square below 960 is 961, and the largest perfect square below 960 is 900. √960 falls somewhere between 30 and 31.</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)</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)</p>
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<p>Going by the formula (960 - 900) ÷ (961-900) = 60/61 ≈ 0.98387 Using the formula, we identified the<a>decimal</a>point of our square root.</p>
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<p>Going by the formula (960 - 900) ÷ (961-900) = 60/61 ≈ 0.98387 Using the formula, we identified the<a>decimal</a>point of our square root.</p>
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<p>The next step is adding the value we got initially to the decimal number which is 30 + 0.98387 = 30.98387, so the square root of 960 is approximately 30.98387.</p>
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<p>The next step is adding the value we got initially to the decimal number which is 30 + 0.98387 = 30.98387, so the square root of 960 is approximately 30.98387.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 960</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 960</h2>
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<p>Students do make mistakes while finding the square root, such as forgetting about the negative square root and skipping long division methods, etc. Now let us look at a few of those mistakes that students tend to make in detail.</p>
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<p>Students do make mistakes while finding the square root, such as forgetting about the negative square root and skipping long division methods, etc. Now let us look at a few of those mistakes that students tend to make in detail.</p>
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<h2>Download Worksheets</h2>
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<h3>Problem 1</h3>
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<h3>Problem 1</h3>
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<p>Can you help Max find the area of a square box if its side length is given as √960?</p>
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<p>Can you help Max find the area of a square box if its side length is given as √960?</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 960 square units.</p>
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<p>The area of the square is approximately 960 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 √960.</p>
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<p>The side length is given as √960.</p>
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<p>Area of the square = side2 = √960 x √960 = 960.</p>
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<p>Area of the square = side2 = √960 x √960 = 960.</p>
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<p>Therefore, the area of the square box is approximately 960 square units.</p>
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<p>Therefore, the area of the square box is approximately 960 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 960 square feet is built; if each of the sides is √960, what will be the square feet of half of the building?</p>
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<p>A square-shaped building measuring 960 square feet is built; if each of the sides is √960, 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>480 square feet.</p>
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<p>480 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 960 by 2 = we get 480.</p>
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<p>Dividing 960 by 2 = we get 480.</p>
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<p>So half of the building measures 480 square feet.</p>
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<p>So half of the building measures 480 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 √960 x 5.</p>
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<p>Calculate √960 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>154.91935</p>
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<p>154.91935</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 960</p>
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<p>The first step is to find the square root of 960</p>
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<p>which is approximately 30.98387, the second step is to multiply 30.98387 with 5.</p>
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<p>which is approximately 30.98387, the second step is to multiply 30.98387 with 5.</p>
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<p>So 30.98387 x 5 = 154.91935.</p>
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<p>So 30.98387 x 5 = 154.91935.</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 (960 + 40)?</p>
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<p>What will be the square root of (960 + 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 approximately 31.62.</p>
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<p>The square root is approximately 31.62.</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,</p>
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<p>To find the square root,</p>
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<p>we need to find the sum of (960 + 40). 960 + 40 = 1000, and then √1000 ≈ 31.62.</p>
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<p>we need to find the sum of (960 + 40). 960 + 40 = 1000, and then √1000 ≈ 31.62.</p>
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<p>Therefore, the square root of (960 + 40) is approximately ±31.62.</p>
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<p>Therefore, the square root of (960 + 40) is approximately ±31.62.</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 √960 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 √960 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 141.96774 units.</p>
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<p>We find the perimeter of the rectangle as approximately 141.96774 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 × (√960 + 40)</p>
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<p>Perimeter = 2 × (√960 + 40)</p>
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<p>= 2 × (30.98387 + 40)</p>
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<p>= 2 × (30.98387 + 40)</p>
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<p>= 2 × 70.98387 = 141.96774 units.</p>
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<p>= 2 × 70.98387 = 141.96774 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 960</h2>
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<h2>FAQ on Square Root of 960</h2>
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<h3>1.What is √960 in its simplest form?</h3>
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<h3>1.What is √960 in its simplest form?</h3>
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<p>The prime factorization of 960 is 2 x 2 x 2 x 2 x 2 x 3 x 5, so the simplest form of √960 = √(2^5 x 3 x 5).</p>
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<p>The prime factorization of 960 is 2 x 2 x 2 x 2 x 2 x 3 x 5, so the simplest form of √960 = √(2^5 x 3 x 5).</p>
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<h3>2.Mention the factors of 960.</h3>
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<h3>2.Mention the factors of 960.</h3>
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<p>Factors of 960 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 160, 192, 240, 320, 480, and 960.</p>
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<p>Factors of 960 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 160, 192, 240, 320, 480, and 960.</p>
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<h3>3.Calculate the square of 960.</h3>
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<h3>3.Calculate the square of 960.</h3>
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<p>We get the square of 960 by multiplying the number by itself, that is 960 x 960 = 921600.</p>
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<p>We get the square of 960 by multiplying the number by itself, that is 960 x 960 = 921600.</p>
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<h3>4.Is 960 a prime number?</h3>
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<h3>4.Is 960 a prime number?</h3>
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<h3>5.960 is divisible by?</h3>
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<h3>5.960 is divisible by?</h3>
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<p>960 has many factors; those are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 160, 192, 240, 320, 480, and 960.</p>
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<p>960 has many factors; those are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 160, 192, 240, 320, 480, and 960.</p>
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<h2>Important Glossaries for the Square Root of 960</h2>
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<h2>Important Glossaries for the Square Root of 960</h2>
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<ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: 42 = 16 and the inverse of the square is the square root that is √16 = 4.</li>
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<ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: 42 = 16 and the inverse of the square is the square root that is √16 = 4.</li>
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</ul><ul><li><strong>Irrational number:</strong>An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero, and p and q are integers.</li>
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</ul><ul><li><strong>Irrational number:</strong>An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero, and p and q are integers.</li>
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</ul><ul><li><strong>Principal square root:</strong>A number has both positive and negative square roots; however, it is always the positive square root that has more prominence due to its uses in the real world. That is the reason it is also known as 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>Prime factorization is the process of expressing a number as the product of its prime factors.</li>
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</ul><ul><li><strong>Prime factorization:</strong>Prime factorization is the process of expressing a number as the product of its prime factors.</li>
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</ul><ul><li><strong>Long division method:</strong>A method used to find the square root of a number by dividing the number into pairs and iteratively finding approximate values.</li>
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</ul><ul><li><strong>Long division method:</strong>A method used to find the square root of a number by dividing the number into pairs and iteratively finding approximate values.</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>