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Original
2026-01-01
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2026-02-21
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<p>226 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 fields such as vehicle design, finance, etc. Here, we will discuss the square root of 12850.</p>
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<h2>What is the Square Root of 12850?</h2>
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<p>The<a>square</a>root is the inverse<a>of</a>the square of a<a>number</a>. 12850 is not a<a>perfect square</a>. The square root of 12850 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √12850, whereas in exponential form it is expressed as (12850)(1/2). √12850 ≈ 113.362, 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 12850</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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<ol><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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</ol><h2>Square Root of 12850 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 12850 is broken down into its prime factors:</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 12850 Breaking it down, we get 2 x 5 x 5 x 257: 21 x 52 x 2571</p>
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<p><strong>Step 2:</strong>Now we have found the prime factors of 12850. The second step is to make pairs of those prime factors. Since 12850 is not a perfect square, the digits of the number can’t be grouped in pairs.</p>
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<p>Therefore, calculating √12850 using prime factorization is not straightforward.</p>
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<h3>Explore Our Programs</h3>
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<h2>Square Root of 12850 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 12850, we need to group it as 50 and 128.</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 12850, we need to group it as 50 and 128.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is ≤ 128. We can say n as ‘11’ because 11 x 11 = 121, which is lesser than 128. Now the<a>quotient</a>is 11, after subtracting 128 - 121, the<a>remainder</a>is 7.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is ≤ 128. We can say n as ‘11’ because 11 x 11 = 121, which is lesser than 128. Now the<a>quotient</a>is 11, after subtracting 128 - 121, the<a>remainder</a>is 7.</p>
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<p><strong>Step 3:</strong>Now let us bring down 50 which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 11 + 11 = 22, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 50 which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 11 + 11 = 22, 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 22n 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 22n 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 22n × n ≤ 750. Let us consider n as 3, now 223 x 3 = 669. Step 6: Subtract 750 from 669, the difference is 81, and the quotient is 113.</p>
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<p><strong>Step 5:</strong>The next step is finding 22n × n ≤ 750. Let us consider n as 3, now 223 x 3 = 669. Step 6: Subtract 750 from 669, the difference is 81, and the quotient is 113.</p>
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<p><strong>Step 7:</strong>Since the remainder is not zero, 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 8100.</p>
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<p><strong>Step 7:</strong>Since the remainder is not zero, 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 8100.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 226 because 226 x 3 = 678.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 226 because 226 x 3 = 678.</p>
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<p><strong>Step 9:</strong>Subtracting 678 from 8100 we get the result 1422.</p>
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<p><strong>Step 9:</strong>Subtracting 678 from 8100 we get the result 1422.</p>
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<p><strong>Step 10:</strong>The quotient is 113.3</p>
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<p><strong>Step 10:</strong>The quotient is 113.3</p>
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<p><strong>Step 11:</strong>Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal values, continue till the remainder is zero.</p>
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<p><strong>Step 11:</strong>Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal values, continue till the remainder is zero.</p>
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<p>So the square root of √12850 is approximately 113.36.</p>
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<p>So the square root of √12850 is approximately 113.36.</p>
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<h2>Square Root of 12850 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 12850 using the approximation method.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √12850. The smallest perfect square<a>less than</a>12850 is 12769 (which is 1132) and the largest perfect square more than 12850 is 12896 (which is 1142). √12850 falls somewhere between 113 and 114.</p>
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<p><strong>Step 2:</strong>Now we need to apply the<a>formula</a>: (Given number - smallest perfect square) / (Larger perfect square - smallest perfect square) Using the formula (12850 - 12769) / (12896 - 12769) = 81 / 127 = 0.6378</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 113 + 0.64 = 113.64, so the square root of 12850 is approximately 113.64.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 12850</h2>
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<p>Students do make mistakes while finding the square root, like forgetting about the negative square root or skipping steps in 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 √12850?</p>
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<p>Okay, lets begin</p>
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<p>The area of the square is approximately 12850 square units.</p>
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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 side length is given as √12850.</p>
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<p>Area of the square = side2 = √12850 x √12850 = 12850.</p>
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<p>Therefore, the area of the square box is approximately 12850 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 12850 square feet is built; if each of the sides is √12850, 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>6425 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.</p>
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<p>Dividing 12850 by 2 gives us 6425.</p>
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<p>So half of the building measures 6425 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 √12850 x 5.</p>
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<p>Okay, lets begin</p>
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<p>Approximately 566.81</p>
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<h3>Explanation</h3>
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<p>The first step is to find the square root of 12850, which is approximately 113.36.</p>
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<p>The second step is to multiply 113.36 by 5.</p>
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<p>So, 113.36 x 5 ≈ 566.81.</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 (12850 + 150)?</p>
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<p>Okay, lets begin</p>
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<p>The square root is approximately 115.04</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 (12850 + 150) = 13000.</p>
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<p>Then, √13000 ≈ 115.04.</p>
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<p>Therefore, the square root of (12850 + 150) is approximately ±115.04.</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 √12850 units and the width ‘w’ is 50 units.</p>
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<p>Okay, lets begin</p>
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<p>We find the perimeter of the rectangle as approximately 326.72 units.</p>
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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 = 2 × (√12850 + 50) = 2 × (113.36 + 50) = 2 × 163.36 ≈ 326.72 units.</p>
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<p>Well explained 👍</p>
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<h2>FAQ on Square Root of 12850</h2>
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<h3>1.What is √12850 in its simplest form?</h3>
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<p>The prime factorization of 12850 is 2 x 5 x 5 x 257, so the simplest form of √12850 is √(2 x 52 x 257).</p>
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<h3>2.Mention the factors of 12850.</h3>
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<p>Factors of 12850 are 1, 2, 5, 10, 25, 50, 257, 514, 1285, 2570, 6425, and 12850.</p>
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<h3>3.Calculate the square of 12850.</h3>
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<p>We get the square of 12850 by multiplying the number by itself, that is 12850 x 12850.</p>
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<h3>4.Is 12850 a prime number?</h3>
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<p>12850 is not a<a>prime number</a>, as it has more than two factors.</p>
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<h3>5.12850 is divisible by?</h3>
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<p>12850 has several factors; those are 1, 2, 5, 10, 25, 50, 257, 514, 1285, 2570, 6425, and 12850.</p>
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<h2>Important Glossaries for the Square Root of 12850</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><ul><li><strong>Irrational number:</strong>An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.</li>
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</ul><ul><li><strong>Principal square root</strong>: A number has both positive and negative square roots; however, it is always the positive square root that has more prominence due to its uses in the real world. That is the reason it is also known as a principal square root.</li>
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</ul><ul><li><strong>Prime factorization:</strong>The expression of a number as a product of its prime factors. Example: 18 = 2 x 32.</li>
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</ul><ul><li><strong>Long division method:</strong>A technique used to find the square root of a non-perfect square by dividing, multiplying, subtracting, and bringing down numbers in steps.</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>