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2026-01-01
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2026-02-28
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<p>225 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 315.</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 315.</p>
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<h2>What is the Square Root of 315?</h2>
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<h2>What is the Square Root of 315?</h2>
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<p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 315 is not a<a>perfect square</a>. The square root of 315 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √315, whereas (315)^(1/2) in the exponential form. √315 ≈ 17.748239, 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>. 315 is not a<a>perfect square</a>. The square root of 315 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √315, whereas (315)^(1/2) in the exponential form. √315 ≈ 17.748239, 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 315</h2>
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<h2>Finding the Square Root of 315</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<a>long 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<a>long 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 315 by Prime Factorization Method</h2>
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</ul><h2>Square Root of 315 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 315 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 315 is broken down into its prime factors:</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 315 Breaking it down, we get 3 x 3 x 5 x 7: 3^2 x 5 x 7</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 315 Breaking it down, we get 3 x 3 x 5 x 7: 3^2 x 5 x 7</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 315. The second step is to make pairs of those prime factors. Since 315 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 315. The second step is to make pairs of those prime factors. Since 315 is not a perfect square, the digits of the number can’t be grouped in pairs.</p>
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<p>Therefore, calculating 315 using prime factorization is impossible.</p>
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<p>Therefore, calculating 315 using prime factorization is impossible.</p>
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<h2>Square Root of 315 by Long Division Method</h2>
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<h2>Square Root of 315 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 315, we need to group it as 15 and 3.</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 315, we need to group it as 15 and 3.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is ≤ 3. We can say n is '1' because 1 x 1 is lesser than or equal to 3. Now the<a>quotient</a>is 1. After subtracting 1 from 3, the<a>remainder</a>is 2.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is ≤ 3. We can say n is '1' because 1 x 1 is lesser than or equal to 3. Now the<a>quotient</a>is 1. After subtracting 1 from 3, the<a>remainder</a>is 2.</p>
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<p><strong>Step 3:</strong>Now let us bring down 15, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 1 + 1 to get 2, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 15, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 1 + 1 to get 2, which will be our new divisor.</p>
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<p><strong>Step 4:</strong>The new divisor will be 2n. Now we need to find the value of n.</p>
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<p><strong>Step 4:</strong>The new divisor will be 2n. Now we need to find the value of n.</p>
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<p><strong>Step 5:</strong>The next step is finding 2n x n ≤ 215. Let us consider n as 7, now 27 x 7 = 189.</p>
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<p><strong>Step 5:</strong>The next step is finding 2n x n ≤ 215. Let us consider n as 7, now 27 x 7 = 189.</p>
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<p><strong>Step 6:</strong>Subtract 189 from 215. The difference is 26, and the quotient is 17.</p>
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<p><strong>Step 6:</strong>Subtract 189 from 215. The difference is 26, and the quotient is 17.</p>
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<p><strong>Step 7:</strong>Since the dividend is<a>less than</a>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 2600.</p>
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<p><strong>Step 7:</strong>Since the dividend is<a>less than</a>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 2600.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 354 because 354 x 7 = 2478.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 354 because 354 x 7 = 2478.</p>
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<p><strong>Step 9:</strong>Subtracting 2478 from 2600, we get the result 122.</p>
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<p><strong>Step 9:</strong>Subtracting 2478 from 2600, we get the result 122.</p>
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<p><strong>Step 10:</strong>Now the quotient is 17.7.</p>
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<p><strong>Step 10:</strong>Now the quotient is 17.7.</p>
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<p><strong>Step 11:</strong>Continue doing these steps until we get two numbers after the decimal point. If there are no decimal values, continue till the remainder is zero.</p>
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<p><strong>Step 11:</strong>Continue doing these steps until we get two numbers after the decimal point. If there are no decimal values, continue till the remainder is zero.</p>
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<p>So the square root of √315 ≈ 17.74.</p>
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<p>So the square root of √315 ≈ 17.74.</p>
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<h2>Square Root of 315 by Approximation Method</h2>
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<h2>Square Root of 315 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 315 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 315 using the approximation method:</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √315.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √315.</p>
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<p>The smallest perfect square less than 315 is 289, and the largest perfect square<a>greater than</a>315 is 324. √315 falls somewhere between 17 and 18.</p>
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<p>The smallest perfect square less than 315 is 289, and the largest perfect square<a>greater than</a>315 is 324. √315 falls somewhere between 17 and 18.</p>
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<p><strong>Step 2:</strong>Now we need to apply the<a>formula</a>: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Going by the formula (315 - 289) / (324 - 289) = 0.74.</p>
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<p><strong>Step 2:</strong>Now we need to apply the<a>formula</a>: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Going by the formula (315 - 289) / (324 - 289) = 0.74.</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 integer part of the square root to the decimal number, which is 17 + 0.74 = 17.74.</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 integer part of the square root to the decimal number, which is 17 + 0.74 = 17.74.</p>
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<p>Therefore, the square root of 315 is approximately 17.74.</p>
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<p>Therefore, the square root of 315 is approximately 17.74.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 315</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 315</h2>
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<p>Students often make mistakes while finding the square root, such as forgetting about the negative square root, skipping long division steps, etc. Now let us look at a few of the common 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, skipping long division steps, etc. Now let us look at a few of the common 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 √315?</p>
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<p>Can you help Max find the area of a square box if its side length is given as √315?</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 315 square units.</p>
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<p>The area of the square is approximately 315 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 √315.</p>
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<p>The side length is given as √315.</p>
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<p>Area of the square = side² = (√315) x (√315) = 315.</p>
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<p>Area of the square = side² = (√315) x (√315) = 315.</p>
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<p>Therefore, the area of the square box is approximately 315 square units.</p>
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<p>Therefore, the area of the square box is approximately 315 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 315 square feet is built; if each of the sides is √315, what will be the square feet of half of the building?</p>
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<p>A square-shaped building measuring 315 square feet is built; if each of the sides is √315, 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>157.5 square feet</p>
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<p>157.5 square feet</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>We can divide the given area by 2 as the building is square-shaped.</p>
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<p>We can divide the given area by 2 as the building is square-shaped.</p>
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<p>Dividing 315 by 2, we get 157.5.</p>
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<p>Dividing 315 by 2, we get 157.5.</p>
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<p>So half of the building measures 157.5 square feet.</p>
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<p>So half of the building measures 157.5 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 √315 x 5.</p>
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<p>Calculate √315 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>Approximately 88.71</p>
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<p>Approximately 88.71</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 315, which is approximately 17.74.</p>
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<p>The first step is to find the square root of 315, which is approximately 17.74.</p>
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<p>The second step is to multiply 17.74 by 5.</p>
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<p>The second step is to multiply 17.74 by 5.</p>
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<p>So, 17.74 x 5 ≈ 88.71.</p>
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<p>So, 17.74 x 5 ≈ 88.71.</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 (315 + 9)?</p>
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<p>What will be the square root of (315 + 9)?</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 ±18.</p>
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<p>The square root is ±18.</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 (315 + 9). 315 + 9 = 324, and √324 = 18.</p>
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<p>To find the square root, we need to find the sum of (315 + 9). 315 + 9 = 324, and √324 = 18.</p>
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<p>Therefore, the square root of (315 + 9) is ±18.</p>
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<p>Therefore, the square root of (315 + 9) is ±18.</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 √315 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 √315 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 75.48 units.</p>
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<p>The perimeter of the rectangle is approximately 75.48 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 × (√315 + 20) ≈ 2 × (17.74 + 20) ≈ 2 × 37.74 ≈ 75.48 units.</p>
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<p>Perimeter = 2 × (√315 + 20) ≈ 2 × (17.74 + 20) ≈ 2 × 37.74 ≈ 75.48 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 315</h2>
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<h2>FAQ on Square Root of 315</h2>
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<h3>1.What is √315 in its simplest form?</h3>
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<h3>1.What is √315 in its simplest form?</h3>
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<p>The prime factorization of 315 is 3 x 3 x 5 x 7, so the simplest form of √315 = √(3^2 x 5 x 7).</p>
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<p>The prime factorization of 315 is 3 x 3 x 5 x 7, so the simplest form of √315 = √(3^2 x 5 x 7).</p>
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<h3>2.Mention the factors of 315.</h3>
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<h3>2.Mention the factors of 315.</h3>
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<p>Factors of 315 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, and 315.</p>
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<p>Factors of 315 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, and 315.</p>
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<h3>3.Calculate the square of 315.</h3>
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<h3>3.Calculate the square of 315.</h3>
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<p>We get the square of 315 by multiplying the number by itself, that is 315 x 315 = 99225.</p>
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<p>We get the square of 315 by multiplying the number by itself, that is 315 x 315 = 99225.</p>
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<h3>4.Is 315 a prime number?</h3>
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<h3>4.Is 315 a prime number?</h3>
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<h3>5.315 is divisible by?</h3>
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<h3>5.315 is divisible by?</h3>
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<p>315 has many factors. It is divisible by 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, and 315.</p>
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<p>315 has many factors. It is divisible by 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, and 315.</p>
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<h2>Important Glossaries for the Square Root of 315</h2>
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<h2>Important Glossaries for the Square Root of 315</h2>
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<ul><li><strong>Square root:</strong>A square root is the inverse of a square. For example, 4² = 16 and the inverse of the square is the square root, which is √16 = 4.</li>
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<ul><li><strong>Square root:</strong>A square root is the inverse of a square. For example, 4² = 16 and the inverse of the square is the square root, which 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>Perfect square:</strong>A perfect square is a number that is the square of an integer. For example, 16 is a perfect square because it is 4².</li>
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</ul><ul><li><strong>Perfect square:</strong>A perfect square is a number that is the square of an integer. For example, 16 is a perfect square because it is 4².</li>
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</ul><ul><li><strong>Long division method:</strong>A method used to find the square root of numbers, especially when they are not perfect squares.</li>
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</ul><ul><li><strong>Long division method:</strong>A method used to find the square root of numbers, especially when they are not perfect squares.</li>
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</ul><ul><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><ul><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>