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2026-01-01
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2026-02-21
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<p>378 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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 25000.</p>
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<h2>What is the Square Root of 25000?</h2>
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<p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 25000 is a<a>perfect square</a>. The square root of 25000 is expressed in both radical and exponential forms. In radical form, it is expressed as √25000, whereas (25000)(1/2) in<a>exponential form</a>. √25000 = 158.113883, which is a<a>rational number</a>because it can 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 25000</h2>
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<p>The<a>prime factorization</a>method can be used for perfect square numbers. For non-perfect squares, the long-<a>division</a>and approximation methods 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 25000 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 25000 is broken down into its prime factors:</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 25000 Breaking it down, we get 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5 x 5: 24 x 55</p>
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<p><strong>Step 2:</strong>Now we found the prime factors of 25000. The second step is to make pairs of those prime factors. Since 25000 is a perfect square, we can pair the digits.</p>
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<p>Therefore, calculating √25000 using prime factorization is possible: √25000 = √(24 x 55) = 22 x 5(5/2) = 100 x 5(1/2) = 100 x 5 = 500</p>
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<h3>Explore Our Programs</h3>
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<h2>Square Root of 25000 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 25000, we group it as 250 and 00.</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 25000, we group it as 250 and 00.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is closest to the first group (250). We can say n as ‘15’ because 15 x 15 = 225, which is<a>less than</a>250. Now the<a>quotient</a>is 15, and after subtracting, the<a>remainder</a>is 25.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is closest to the first group (250). We can say n as ‘15’ because 15 x 15 = 225, which is<a>less than</a>250. Now the<a>quotient</a>is 15, and after subtracting, the<a>remainder</a>is 25.</p>
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<p><strong>Step 3:</strong>Now let us bring down 00, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 15 + 15, we get 30, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 00, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 15 + 15, we get 30, 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 30n 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 sum of the dividend and quotient. Now we get 30n 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 30n × n ≤ 2500. Let us consider n as 8; now 30 x 8 x 8 = 2400.</p>
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<p><strong>Step 5:</strong>The next step is finding 30n × n ≤ 2500. Let us consider n as 8; now 30 x 8 x 8 = 2400.</p>
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<p><strong>Step 6:</strong>Subtract 2500 from 2400; the difference is 100, and the quotient is 158.</p>
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<p><strong>Step 6:</strong>Subtract 2500 from 2400; the difference is 100, and the quotient is 158.</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 zeroes to the dividend. Now the new dividend is 10000.</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 zeroes to the dividend. Now the new dividend is 10000.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor, which is 316, because 316 x 3 = 948.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor, which is 316, because 316 x 3 = 948.</p>
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<p><strong>Step 9:</strong>Subtracting 948 from 1000, we get the result 52.</p>
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<p><strong>Step 9:</strong>Subtracting 948 from 1000, we get the result 52.</p>
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<p><strong>Step 10:</strong>Now the quotient is 158.11.</p>
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<p><strong>Step 10:</strong>Now the quotient is 158.11.</p>
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<p><strong>Step 11:</strong>Continue doing these steps until we get two numbers after the decimal point. So the square root of √25000 is 158.11.</p>
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<p><strong>Step 11:</strong>Continue doing these steps until we get two numbers after the decimal point. So the square root of √25000 is 158.11.</p>
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<h2>Square Root of 25000 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 25000 using the approximation method.</p>
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<p><strong>Step 1:</strong>We have to find the closest perfect square of √25000. The smallest perfect square less than 25000 is 22500, and the largest perfect square<a>greater than</a>25000 is 25600. √25000 falls somewhere between 150 and 160.</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)</p>
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<p>Using the formula (25000 - 22500) ÷ (25600 - 22500) = 0.8 Using the formula, we identified the<a>decimal</a>point of our square root.</p>
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<p>The next step is adding the value we got initially to the decimal number, which is 150 + 0.8 = 150.8, so the approximate square root of 25000 is 150.8.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 25000</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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<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 √2500?</p>
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<p>Okay, lets begin</p>
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<p>The area of the square is 2500 square units.</p>
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<h3>Explanation</h3>
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<p>The area of a square = side2.</p>
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<p>The side length is given as √2500.</p>
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<p>Area of the square = side2 = √2500 x √2500 = 50 x 50 = 2500.</p>
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<p>Therefore, the area of the square box is 2500 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 25000 square feet is built; if each of the sides is √25000, 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>12500 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 25000 by 2 = we get 12500.</p>
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<p>So half of the building measures 12500 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 √25000 x 5.</p>
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<p>Okay, lets begin</p>
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<p>790.569415</p>
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<h3>Explanation</h3>
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<p>The first step is to find the square root of 25000, which is 158.11.</p>
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<p>The second step is to multiply 158.11 with 5.</p>
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<p>So 158.11 x 5 = 790.569415.</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 (25000 + 100)?</p>
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<p>Okay, lets begin</p>
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<p>The square root is 158.49.</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 (25000 + 100).</p>
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<p>25000 + 100 = 25100, and then √25100 ≈ 158.49.</p>
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<p>Therefore, the square root of (25000 + 100) is approximately 158.49.</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 √2500 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 176 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 × (√2500 + 38) = 2 × (50 + 38) = 2 × 88 = 176 units.</p>
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<p>Well explained 👍</p>
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<h2>FAQ on Square Root of 25000</h2>
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<h3>1.What is √25000 in its simplest form?</h3>
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<p>The prime factorization of 25000 is 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5 x 5, so the simplest form of √25000 = √(24 x 55).</p>
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<h3>2.Mention the factors of 25000.</h3>
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<p>Factors of 25000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 625, 1000, 1250, 2500, 5000, 12500, and 25000.</p>
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<h3>3.Calculate the square of 25000.</h3>
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<p>We get the square of 25000 by multiplying the number by itself, that is 25000 x 25000 = 625000000.</p>
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<h3>4.Is 25000 a prime number?</h3>
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<p>25000 is not a<a>prime number</a>, as it has more than two factors.</p>
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<h3>5.25000 is divisible by?</h3>
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<p>25000 has many factors; those are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 625, 1000, 1250, 2500, 5000, 12500, and 25000.</p>
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<h2>Important Glossaries for the Square Root of 25000</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>Rational number:</strong>A rational number is a number that can 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 product of an integer multiplied by itself. Example: 16 is a perfect square because it is 4 x 4.</li>
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</ul><ul><li><strong>Exponent:</strong>An exponent refers to the number of times a number is multiplied by itself. Example: 2^3 means 2 x 2 x 2.</li>
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</ul><ul><li><strong>Approximation:</strong>Approximation is a method of finding a value that is close enough to the right answer, usually with some thought or consideration.</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>