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2026-01-01
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2026-02-28
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<p>224 Learners</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, finance, etc. Here, we will discuss the square root of 7825.</p>
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<h2>What is the Square Root of 7825?</h2>
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<p>The<a>square</a>root is the inverse<a>of</a>the square of a<a>number</a>. 7825 is not a<a>perfect square</a>. The square root of 7825 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √7825, whereas (7825)^(1/2) in the exponential form. √7825 ≈ 88.436, 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 7825</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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<ul><li>Prime factorization method</li>
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<li>Long division method</li>
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<li>Approximation method</li>
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</ul><h2>Square Root of 7825 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 7825 is broken down into its prime factors.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 7825 Breaking it down, we get 5 x 5 x 313: \(5^2 \times 313^1\)</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 7825. The second step is to make pairs of those prime factors. Since 7825 is not a perfect square, the digits of the number can’t be grouped in pairs. Therefore, calculating 7825 using prime factorization is impossible.</p>
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<h2>Square Root of 7825 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 7825, we group it as 78 and 25.</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 7825, we group it as 78 and 25.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is 64. We can say n as ‘8’ because 8 x 8 is lesser than or equal to 78. Now the<a>quotient</a>is 8 after subtracting 64 from 78, the<a>remainder</a>is 14</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is 64. We can say n as ‘8’ because 8 x 8 is lesser than or equal to 78. Now the<a>quotient</a>is 8 after subtracting 64 from 78, the<a>remainder</a>is 14</p>
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<p><strong>Step 3:</strong>Now let us bring down 25 which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 8 + 8 we get 16 which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 25 which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 8 + 8 we get 16 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 16n 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 16n 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 16n x n ≤ 1425. Let us consider n as 8, now 16 x 8 + 8 = 136 Step 6: Subtract 136 from 1425, the difference is 89, and the quotient is 88.</p>
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<p><strong>Step 5:</strong>The next step is finding 16n x n ≤ 1425. Let us consider n as 8, now 16 x 8 + 8 = 136 Step 6: Subtract 136 from 1425, the difference is 89, and the quotient is 88.</p>
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<p><strong>Step 7:</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 zeros to the dividend. Now the new dividend is 8900.</p>
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<p><strong>Step 7:</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 zeros to the dividend. Now the new dividend is 8900.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 883 because 883 x 10 = 8830.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 883 because 883 x 10 = 8830.</p>
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<p><strong>Step 9:</strong>Subtracting 8830 from 8900 we get the result 70.</p>
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<p><strong>Step 9:</strong>Subtracting 8830 from 8900 we get the result 70.</p>
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<p><strong>Step 10:</strong>Now the quotient is 88.4.</p>
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<p><strong>Step 10:</strong>Now the quotient is 88.4.</p>
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<p><strong>Step 11:</strong>Continue doing these steps until we get two numbers after the decimal point. Suppose there are no decimal values, continue till the remainder is zero. So the square root of √7825 ≈ 88.44.</p>
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<p><strong>Step 11:</strong>Continue doing these steps until we get two numbers after the decimal point. Suppose there are no decimal values, continue till the remainder is zero. So the square root of √7825 ≈ 88.44.</p>
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<h2>Square Root of 7825 by Approximation Method</h2>
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<p>The 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 7825 using the approximation method.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √7825. The smallest perfect square near 7825 is 7744 and the largest perfect square near 7825 is 7921. √7825 falls somewhere between 88 and 89.</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 (7825 - 7744) / (7921 - 7744) = 81 / 177 = 0.457 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 88 + 0.457 = 88.457, so the square root of 7825 is approximately 88.457.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 7825</h2>
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<p>Students do make mistakes while finding the square root, similarly forgetting about the negative square root or 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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<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 √7825?</p>
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<p>Okay, lets begin</p>
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<p>The area of the square is 7825 square units.</p>
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<h3>Explanation</h3>
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<p>The area of the square = side². The side length is given as √7825. Area of the square = side² = √7825 x √7825 = 7825. Therefore, the area of the square box is 7825 square units.</p>
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<p>Well explained 👍</p>
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<h3>Problem 2</h3>
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<p>A square-shaped building measuring 7825 square feet is built; if each of the sides is √7825, 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>3912.5 square feet</p>
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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 7825 by 2 = we get 3912.5 So half of the building measures 3912.5 square feet.</p>
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<p>Well explained 👍</p>
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<h3>Problem 3</h3>
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<p>Calculate √7825 x 5.</p>
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<p>Okay, lets begin</p>
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<p>442.18</p>
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<h3>Explanation</h3>
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<p>The first step is to find the square root of 7825, which is approximately 88.44. The second step is to multiply 88.44 with 5. So, 88.44 x 5 = 442.18.</p>
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<p>Well explained 👍</p>
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<h3>Problem 4</h3>
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<p>What will be the square root of (7825 + 6)?</p>
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<p>Okay, lets begin</p>
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<p>The square root is approximately 88.470</p>
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<h3>Explanation</h3>
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<p>To find the square root, we need to find the sum of (7825 + 6): 7825 + 6 = 7831, and then √7831 ≈ 88.470. Therefore, the square root of (7825 + 6) is approximately ±88.470.</p>
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<p>Well explained 👍</p>
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<h3>Problem 5</h3>
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<p>Find the perimeter of the rectangle if its length ‘l’ is √7825 units and the width ‘w’ is 38 units.</p>
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<p>Okay, lets begin</p>
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<p>We find the perimeter of the rectangle as 253.88 units.</p>
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<h3>Explanation</h3>
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<p>Perimeter of the rectangle = 2 × (length + width) Perimeter = 2 × (√7825 + 38) = 2 × (88.44 + 38) = 2 × 126.44 = 253.88 units.</p>
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<p>Well explained 👍</p>
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<h2>FAQ on Square Root of 7825</h2>
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<h3>1.What is √7825 in its simplest form?</h3>
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<p>The prime factorization of 7825 is 5 x 5 x 313, so the simplest form of √7825 is √(5 x 5 x 313).</p>
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<h3>2.Mention the factors of 7825.</h3>
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<p>Factors of 7825 are 1, 5, 25, 313, 1565, and 7825.</p>
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<h3>3.Calculate the square of 7825.</h3>
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<p>We get the square of 7825 by multiplying the number by itself, that is 7825 x 7825 = 61256225.</p>
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<h3>4.Is 7825 a prime number?</h3>
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<p>7825 is not a<a>prime number</a>, as it has more than two factors.</p>
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<h3>5.7825 is divisible by?</h3>
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<p>7825 has several factors; those are 1, 5, 25, 313, 1565, and 7825.</p>
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<h2>Important Glossaries for the Square Root of 7825</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, which 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>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>Long division method:</strong>A method used to find the square root of non-perfect squares by a series of division steps to approximate the root value. </li>
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<li><strong>Approximation method:</strong>A technique to estimate the square root of a number by using nearby perfect squares to find a closer value.</li>
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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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<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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<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>