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2026-01-01
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2026-02-28
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<p>291 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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 924.</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 924.</p>
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<h2>What is the Square Root of 924?</h2>
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<h2>What is the Square Root of 924?</h2>
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<p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 924 is not a<a>perfect square</a>. The square root of 924 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √924, whereas 924^(1/2) in the exponential form. √924 ≈ 30.396, which is an<a>irrational number</a>because it cannot be expressed in the form of p/q, where p and q are<a>integers</a>and q ≠ 0.</p>
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<p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 924 is not a<a>perfect square</a>. The square root of 924 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √924, whereas 924^(1/2) in the exponential form. √924 ≈ 30.396, 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 924</h2>
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<h2>Finding the Square Root of 924</h2>
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<p>The<a>prime factorization</a>method is used for perfect square numbers. However, for non-perfect square numbers like 924, the<a>long division</a>method and approximation method are used. Let us now learn these methods:</p>
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<p>The<a>prime factorization</a>method is used for perfect square numbers. However, for non-perfect square numbers like 924, the<a>long division</a>method and approximation method are used. Let us now learn these 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 924 by Prime Factorization Method</h2>
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</ul><h2>Square Root of 924 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 924 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 924 is broken down into its prime factors.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 924 Breaking it down, we get 2 x 2 x 3 x 7 x 11: 2^2 x 3^1 x 7^1 x 11^1</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 924 Breaking it down, we get 2 x 2 x 3 x 7 x 11: 2^2 x 3^1 x 7^1 x 11^1</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 924. The second step is to make pairs of those prime factors. Since 924 is not a perfect square, the digits of the number can’t be grouped in pairs.</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 924. The second step is to make pairs of those prime factors. Since 924 is not a perfect square, the digits of the number can’t be grouped in pairs.</p>
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<p>Therefore, calculating 924 using prime factorization alone is not straightforward.</p>
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<p>Therefore, calculating 924 using prime factorization alone is not straightforward.</p>
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<h2>Square Root of 924 by Long Division Method</h2>
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<h2>Square Root of 924 by Long Division Method</h2>
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<p>The long<a>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 long<a>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 924, we need to group it as 24 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 924, we need to group it as 24 and 9.</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 9. We can say n is 3 because 3^2 is 9, which is equal to 9. Now the<a>quotient</a>is 3, after subtracting 9 from 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<a>less than</a>or equal to 9. We can say n is 3 because 3^2 is 9, which is equal to 9. Now the<a>quotient</a>is 3, after subtracting 9 from 9, the<a>remainder</a>is 0.</p>
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<p><strong>Step 3:</strong>Now let us bring down 24, 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 24, 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 sum of the dividend and quotient. Now we get 6n as the new divisor, and we need to find the value of n.</p>
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<p><strong>Step 4:</strong>The new divisor will be the sum of the dividend and quotient. Now we get 6n as the new divisor, and we need to find the value of n.</p>
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<p><strong>Step 5:</strong>The next step is finding 6n × n ≤ 24. Let us consider n as 4; now 6 × 4 = 24.</p>
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<p><strong>Step 5:</strong>The next step is finding 6n × n ≤ 24. Let us consider n as 4; now 6 × 4 = 24.</p>
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<p><strong>Step 6:</strong>Subtract 24 from 24, and the difference is 0, so the quotient is 34.</p>
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<p><strong>Step 6:</strong>Subtract 24 from 24, and the difference is 0, so the quotient is 34.</p>
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<p><strong>Step 7:</strong>Since we have reached a remainder of 0, the square root of 924 is approximately 30.396 when continued further, adding decimal places for precision.</p>
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<p><strong>Step 7:</strong>Since we have reached a remainder of 0, the square root of 924 is approximately 30.396 when continued further, adding decimal places for precision.</p>
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<h2>Square Root of 924 by Approximation Method</h2>
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<h2>Square Root of 924 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 924 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 924 using the approximation method.</p>
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<p><strong>Step 1:</strong>Now, we have to find the closest perfect square of √924.</p>
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<p><strong>Step 1:</strong>Now, we have to find the closest perfect square of √924.</p>
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<p>The smallest perfect square less than 924 is 900, and the largest perfect square<a>greater than</a>924 is 961.</p>
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<p>The smallest perfect square less than 924 is 900, and the largest perfect square<a>greater than</a>924 is 961.</p>
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<p>√924 falls somewhere between 30 and 31.</p>
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<p>√924 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>:</p>
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<p><strong>Step 2:</strong>Now we need to apply the<a>formula</a>:</p>
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<p>(Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).</p>
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<p>(Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).</p>
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<p>Using the formula, (924 - 900) / (961 - 900) = 24 / 61 ≈ 0.393</p>
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<p>Using the formula, (924 - 900) / (961 - 900) = 24 / 61 ≈ 0.393</p>
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<p>Adding the integer part we identified initially to the<a>decimal</a>number: 30 + 0.393 ≈ 30.393, so the square root of 924 is approximately 30.396.</p>
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<p>Adding the integer part we identified initially to the<a>decimal</a>number: 30 + 0.393 ≈ 30.393, so the square root of 924 is approximately 30.396.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 924</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 924</h2>
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<p>Students do make mistakes while finding the square root, such as forgetting about the negative square root, skipping long division methods, etc. Now let us look at a few of those mistakes that students tend to make in detail.</p>
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<p>Students do make mistakes while finding the square root, such as forgetting about the negative square root, skipping long division methods, etc. Now let us look at a few of those mistakes that students tend to make in detail.</p>
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<h2>Download Worksheets</h2>
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<h3>Problem 1</h3>
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<h3>Problem 1</h3>
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<p>Can you help Max find the area of a square box if its side length is given as √924?</p>
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<p>Can you help Max find the area of a square box if its side length is given as √924?</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 854.976 square units.</p>
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<p>The area of the square is approximately 854.976 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. The side length is given as √924. Area of the square = side² = √924 × √924 ≈ 30.396 × 30.396 ≈ 924 Therefore, the area of the square box is approximately 924 square units.</p>
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<p>The area of the square = side². The side length is given as √924. Area of the square = side² = √924 × √924 ≈ 30.396 × 30.396 ≈ 924 Therefore, the area of the square box is approximately 924 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 924 square feet is built; if each of the sides is √924, what will be the square feet of half of the building?</p>
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<p>A square-shaped building measuring 924 square feet is built; if each of the sides is √924, 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>462 square feet</p>
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<p>462 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 924 by 2 = we get 462. So half of the building measures 462 square feet.</p>
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<p>We can just divide the given area by 2 as the building is square-shaped. Dividing 924 by 2 = we get 462. So half of the building measures 462 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 √924 × 5.</p>
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<p>Calculate √924 × 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 151.98</p>
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<p>Approximately 151.98</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 924, which is approximately 30.396. The second step is to multiply 30.396 by 5. So 30.396 × 5 ≈ 151.98.</p>
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<p>The first step is to find the square root of 924, which is approximately 30.396. The second step is to multiply 30.396 by 5. So 30.396 × 5 ≈ 151.98.</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 (924 + 76)?</p>
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<p>What will be the square root of (924 + 76)?</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 31.</p>
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<p>The square root is 31.</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 (924 + 76). 924 + 76 = 1000, and then √1000 ≈ 31.622. Therefore, the square root of (924 + 76) is approximately ±31.622.</p>
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<p>To find the square root, we need to find the sum of (924 + 76). 924 + 76 = 1000, and then √1000 ≈ 31.622. Therefore, the square root of (924 + 76) is approximately ±31.622.</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 √924 units and the width ‘w’ is 45 units.</p>
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<p>Find the perimeter of the rectangle if its length ‘l’ is √924 units and the width ‘w’ is 45 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 150.792 units.</p>
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<p>We find the perimeter of the rectangle as approximately 150.792 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 × (√924 + 45) ≈ 2 × (30.396 + 45) ≈ 2 × 75.396 ≈ 150.792 units.</p>
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<p>Perimeter of the rectangle = 2 × (length + width) Perimeter = 2 × (√924 + 45) ≈ 2 × (30.396 + 45) ≈ 2 × 75.396 ≈ 150.792 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 924</h2>
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<h2>FAQ on Square Root of 924</h2>
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<h3>1.What is √924 in its simplest form?</h3>
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<h3>1.What is √924 in its simplest form?</h3>
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<p>The prime factorization of 924 is 2 × 2 × 3 × 7 × 11, so the simplest form of √924 ≈ 30.396.</p>
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<p>The prime factorization of 924 is 2 × 2 × 3 × 7 × 11, so the simplest form of √924 ≈ 30.396.</p>
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<h3>2.Mention the factors of 924.</h3>
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<h3>2.Mention the factors of 924.</h3>
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<p>Factors of 924 are 1, 2, 3, 4, 6, 7, 11, 12, 14, 21, 22, 28, 33, 42, 44, 66, 77, 84, 132, 154, 231, 308, 462, and 924.</p>
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<p>Factors of 924 are 1, 2, 3, 4, 6, 7, 11, 12, 14, 21, 22, 28, 33, 42, 44, 66, 77, 84, 132, 154, 231, 308, 462, and 924.</p>
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<h3>3.Calculate the square of 924.</h3>
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<h3>3.Calculate the square of 924.</h3>
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<p>We get the square of 924 by multiplying the number by itself, that is 924 × 924 = 853776.</p>
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<p>We get the square of 924 by multiplying the number by itself, that is 924 × 924 = 853776.</p>
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<h3>4.Is 924 a prime number?</h3>
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<h3>4.Is 924 a prime number?</h3>
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<h3>5.924 is divisible by?</h3>
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<h3>5.924 is divisible by?</h3>
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<p>924 has many factors; those are 1, 2, 3, 4, 6, 7, 11, 12, 14, 21, 22, 28, 33, 42, 44, 66, 77, 84, 132, 154, 231, 308, 462, and 924.</p>
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<p>924 has many factors; those are 1, 2, 3, 4, 6, 7, 11, 12, 14, 21, 22, 28, 33, 42, 44, 66, 77, 84, 132, 154, 231, 308, 462, and 924.</p>
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<h2>Important Glossaries for the Square Root of 924</h2>
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<h2>Important Glossaries for the Square Root of 924</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>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 use in the real world. That is the reason it is also known as the principal square root. </li>
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<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 use in the real world. That is the reason it is also known as the principal square root. </li>
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<li><strong>Prime factorization:</strong>Prime factorization is the process of breaking down a number into its prime factors. For example, the prime factorization of 924 is 2 × 2 × 3 × 7 × 11. </li>
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<li><strong>Prime factorization:</strong>Prime factorization is the process of breaking down a number into its prime factors. For example, the prime factorization of 924 is 2 × 2 × 3 × 7 × 11. </li>
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<li><strong>Decimal:</strong>If a number has a whole number and a fraction in a single number, then it is called a decimal. For example, 7.86, 8.65, and 9.42 are decimals.</li>
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<li><strong>Decimal:</strong>If a number has a whole number and a fraction in a single number, then it is called a decimal. For example, 7.86, 8.65, and 9.42 are decimals.</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>