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2026-01-01
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2026-02-28
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<p>205 Learners</p>
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<p>Last updated on<strong>September 29, 2025</strong></p>
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<p>Last updated on<strong>September 29, 2025</strong></p>
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<p>If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in fields such as vehicle design, finance, etc. Here, we will discuss the square root of 504.</p>
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<p>If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in fields such as vehicle design, finance, etc. Here, we will discuss the square root of 504.</p>
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<h2>What is the Square Root of 504?</h2>
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<h2>What is the Square Root of 504?</h2>
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<p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 504 is not a<a>perfect square</a>. The square root of 504 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √504, whereas (504)^(1/2) in the exponential form. √504 ≈ 22.44994, 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>. 504 is not a<a>perfect square</a>. The square root of 504 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √504, whereas (504)^(1/2) in the exponential form. √504 ≈ 22.44994, 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 504</h2>
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<h2>Finding the Square Root of 504</h2>
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<p>The<a>prime factorization</a>method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where the long-<a>division</a>method and approximation method are used. Let us now learn the following methods:</p>
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<p>The<a>prime factorization</a>method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where the long-<a>division</a>method and approximation method are used. Let us now learn the following methods:</p>
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<ul><li>Prime factorization method</li>
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<ul><li>Prime factorization method</li>
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<li>Long division method</li>
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<li>Long division method</li>
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<li>Approximation method</li>
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<li>Approximation method</li>
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</ul><h2>Square Root of 504 by Prime Factorization Method</h2>
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</ul><h2>Square Root of 504 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 504 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 504 is broken down into its prime factors.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 504</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 504</p>
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<p>Breaking it down, we get 2 × 2 × 2 × 3 × 3 × 7: 2^3 × 3^2 × 7</p>
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<p>Breaking it down, we get 2 × 2 × 2 × 3 × 3 × 7: 2^3 × 3^2 × 7</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 504. The second step is to make pairs of those prime factors. Since 504 is not a perfect square, therefore the digits of the number can’t be grouped into pairs. Therefore, calculating 504 using prime factorization is impossible.</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 504. The second step is to make pairs of those prime factors. Since 504 is not a perfect square, therefore the digits of the number can’t be grouped into pairs. Therefore, calculating 504 using prime factorization is impossible.</p>
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<h2>Square Root of 504 by Long Division Method</h2>
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<h2>Square Root of 504 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 504, we need to group it as 04 and 50.</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 504, we need to group it as 04 and 50.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is closest to or<a>less than</a>50. We can say n is '7' because 7 × 7 = 49, which is less than 50. After subtracting 50 - 49, the<a>remainder</a>is 1.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is closest to or<a>less than</a>50. We can say n is '7' because 7 × 7 = 49, which is less than 50. After subtracting 50 - 49, the<a>remainder</a>is 1.</p>
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<p><strong>Step 3:</strong>Bring down 04 to get 104 as the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 7 + 7 to get 14, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Bring down 04 to get 104 as the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 7 + 7 to get 14, which will be our new divisor.</p>
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<p><strong>Step 4:</strong>The new divisor is 14n. We need to find the value of n where 14n × n ≤ 104. Let us consider n as 7, now 147 × 7 = 1029.</p>
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<p><strong>Step 4:</strong>The new divisor is 14n. We need to find the value of n where 14n × n ≤ 104. Let us consider n as 7, now 147 × 7 = 1029.</p>
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<p><strong>Step 5:</strong>Subtract 1040 from 1029, the difference is 11. The<a>quotient</a>is 22.4 so far.</p>
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<p><strong>Step 5:</strong>Subtract 1040 from 1029, the difference is 11. The<a>quotient</a>is 22.4 so far.</p>
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<p><strong>Step 6:</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 1100.</p>
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<p><strong>Step 6:</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 1100.</p>
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<p><strong>Step 7:</strong>Now we need to find the new divisor that is 22 because 224 × 22 = 11000.</p>
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<p><strong>Step 7:</strong>Now we need to find the new divisor that is 22 because 224 × 22 = 11000.</p>
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<p><strong>Step 8:</strong>Subtracting 11000 from 1100 gives us a result of 0.</p>
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<p><strong>Step 8:</strong>Subtracting 11000 from 1100 gives us a result of 0.</p>
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<p><strong>Step 9:</strong>Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal value, continue till the remainder is zero.</p>
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<p><strong>Step 9:</strong>Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal value, continue till the remainder is zero.</p>
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<p>So the square root of √504 is approximately 22.45.</p>
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<p>So the square root of √504 is approximately 22.45.</p>
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<h2>Square Root of 504 by Approximation Method</h2>
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<h2>Square Root of 504 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 504 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 504 using the approximation method.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect squares of √504. The smallest perfect square less than 504 is 484, and the largest perfect square more than 504 is 529. √504 falls somewhere between 22 and 23.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect squares of √504. The smallest perfect square less than 504 is 484, and the largest perfect square more than 504 is 529. √504 falls somewhere between 22 and 23.</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 (504 - 484) ÷ (529 - 484) = 20 ÷ 45 ≈ 0.444</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 (504 - 484) ÷ (529 - 484) = 20 ÷ 45 ≈ 0.444</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 22 + 0.444 = 22.444.</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 22 + 0.444 = 22.444.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 504</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 504</h2>
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<p>Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division methods. Now let us look at a few of those mistakes that students tend to make in detail.</p>
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<p>Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division methods. Now let us look at a few of those mistakes that students tend to make in detail.</p>
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<h2>Download Worksheets</h2>
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<h3>Problem 1</h3>
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<h3>Problem 1</h3>
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<p>Can you help Max find the area of a square box if its side length is given as √504?</p>
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<p>Can you help Max find the area of a square box if its side length is given as √504?</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 504 square units.</p>
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<p>The area of the square is approximately 504 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 √504.</p>
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<p>The side length is given as √504.</p>
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<p>Area of the square = side² = √504 × √504 = 504.</p>
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<p>Area of the square = side² = √504 × √504 = 504.</p>
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<p>Therefore, the area of the square box is approximately 504 square units.</p>
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<p>Therefore, the area of the square box is approximately 504 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 field measuring 504 square feet is built; if each of the sides is √504, what will be the square feet of half of the field?</p>
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<p>A square-shaped field measuring 504 square feet is built; if each of the sides is √504, what will be the square feet of half of the field?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>252 square feet</p>
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<p>252 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 field is square-shaped.</p>
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<p>We can just divide the given area by 2 as the field is square-shaped.</p>
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<p>Dividing 504 by 2, we get 252.</p>
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<p>Dividing 504 by 2, we get 252.</p>
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<p>So half of the field measures 252 square feet.</p>
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<p>So half of the field measures 252 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 √504 × 3.</p>
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<p>Calculate √504 × 3.</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 67.35</p>
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<p>Approximately 67.35</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 504, which is approximately 22.45.</p>
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<p>The first step is to find the square root of 504, which is approximately 22.45.</p>
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<p>The second step is to multiply 22.45 by 3.</p>
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<p>The second step is to multiply 22.45 by 3.</p>
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<p>So, 22.45 × 3 ≈ 67.35.</p>
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<p>So, 22.45 × 3 ≈ 67.35.</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 (504 + 5)?</p>
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<p>What will be the square root of (504 + 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>The square root is approximately 22.56.</p>
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<p>The square root is approximately 22.56.</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 (504 + 5). 504 + 5 = 509, and then √509 ≈ 22.56.</p>
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<p>To find the square root, we need to find the sum of (504 + 5). 504 + 5 = 509, and then √509 ≈ 22.56.</p>
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<p>Therefore, the square root of (504 + 5) is approximately ±22.56.</p>
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<p>Therefore, the square root of (504 + 5) is approximately ±22.56.</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 √504 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 √504 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>The perimeter of the rectangle is approximately 124.9 units.</p>
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<p>The perimeter of the rectangle is approximately 124.9 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 × (√504 + 40) = 2 × (22.45 + 40) = 2 × 62.45 = 124.9 units.</p>
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<p>Perimeter = 2 × (√504 + 40) = 2 × (22.45 + 40) = 2 × 62.45 = 124.9 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 504</h2>
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<h2>FAQ on Square Root of 504</h2>
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<h3>1.What is √504 in its simplest form?</h3>
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<h3>1.What is √504 in its simplest form?</h3>
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<p>The prime factorization of 504 is 2 × 2 × 2 × 3 × 3 × 7, so the simplest form of √504 is √(2^3 × 3^2 × 7).</p>
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<p>The prime factorization of 504 is 2 × 2 × 2 × 3 × 3 × 7, so the simplest form of √504 is √(2^3 × 3^2 × 7).</p>
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<h3>2.Mention the factors of 504.</h3>
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<h3>2.Mention the factors of 504.</h3>
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<p>Factors of 504 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, and 504.</p>
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<p>Factors of 504 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, and 504.</p>
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<h3>3.Calculate the square of 504.</h3>
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<h3>3.Calculate the square of 504.</h3>
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<p>We get the square of 504 by multiplying the number by itself, that is 504 × 504 = 254016.</p>
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<p>We get the square of 504 by multiplying the number by itself, that is 504 × 504 = 254016.</p>
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<h3>4.Is 504 a prime number?</h3>
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<h3>4.Is 504 a prime number?</h3>
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<h3>5.504 is divisible by?</h3>
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<h3>5.504 is divisible by?</h3>
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<p>504 has many factors; those are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, and 504.</p>
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<p>504 has many factors; those are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, and 504.</p>
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<h2>Important Glossaries for the Square Root of 504</h2>
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<h2>Important Glossaries for the Square Root of 504</h2>
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<ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: 4^2 = 16 and the inverse of the square is the square root that is √16 = 4. </li>
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<ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: 4^2 = 16 and the inverse of the square is the square root that is √16 = 4. </li>
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<li><strong>Irrational number:</strong>An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers. </li>
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<li><strong>Irrational number:</strong>An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers. </li>
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<li><strong>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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<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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<li><strong>Prime factorization:</strong>The expression of a number as the product of its prime factors. Example: The prime factorization of 504 is 2^3 × 3^2 × 7. </li>
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<li><strong>Prime factorization:</strong>The expression of a number as the product of its prime factors. Example: The prime factorization of 504 is 2^3 × 3^2 × 7. </li>
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<li><strong>Long division method:</strong>A step-by-step process to find the square root of a number by dividing and finding the quotient, used especially for non-perfect squares.</li>
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<li><strong>Long division method:</strong>A step-by-step process to find the square root of a number by dividing and finding the quotient, used especially for 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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<p>▶</p>
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<h2>Jaskaran Singh Saluja</h2>
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<h2>Jaskaran Singh Saluja</h2>
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<h3>About the Author</h3>
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<h3>About the Author</h3>
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<p>Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.</p>
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<p>Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.</p>
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<h3>Fun Fact</h3>
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<h3>Fun Fact</h3>
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<p>: He loves to play the quiz with kids through algebra to make kids love it.</p>
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<p>: He loves to play the quiz with kids through algebra to make kids love it.</p>