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2026-01-01
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2026-02-28
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<p>251 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 1250.</p>
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<h2>What is the Square Root of 1250?</h2>
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<p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 1250 is not a<a>perfect square</a>. The square root of 1250 is expressed in both radical and exponential forms. In the radical form, it is expressed as √1250, whereas (1250)^(1/2) in the<a>exponential form</a>. √1250 ≈ 35.3553, 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 1250</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 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 1250 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 1250 is broken down into its prime factors:</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 1250 Breaking it down, we get 2 x 5 x 5 x 5 x 5: 2^1 x 5^4</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 1250. The second step is to make pairs of those prime factors. Since 1250 is not a perfect square, the digits of the number can’t be grouped perfectly in pairs.</p>
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<p>Therefore, calculating the exact<a>square root</a>of 1250 using prime factorization is not feasible.</p>
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<h3>Explore Our Programs</h3>
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<p>No Courses Available</p>
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<h2>Square Root of 1250 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 square root 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 square root 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 1250, we need to group it as 50 and 12.</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 1250, we need to group it as 50 and 12.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is<a>less than</a>or equal to 12. We can say n as ‘3’ because 3 x 3 = 9, which is less than 12. Now the<a>quotient</a>is 3, and after subtracting 9 from 12, the<a>remainder</a>is 3.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is<a>less than</a>or equal to 12. We can say n as ‘3’ because 3 x 3 = 9, which is less than 12. Now the<a>quotient</a>is 3, and after subtracting 9 from 12, the<a>remainder</a>is 3.</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 3 + 3 = 6, 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 3 + 3 = 6, which will be our new divisor.</p>
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<p><strong>Step 4:</strong>The new divisor will be 6n. We need to find a value for n such that 6n x n ≤ 350. Let n be 5, now 65 x 5 = 325.</p>
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<p><strong>Step 4:</strong>The new divisor will be 6n. We need to find a value for n such that 6n x n ≤ 350. Let n be 5, now 65 x 5 = 325.</p>
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<p><strong>Step 5:</strong>Subtract 325 from 350; the difference is 25, and the quotient is 35.</p>
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<p><strong>Step 5:</strong>Subtract 325 from 350; the difference is 25, and the quotient is 35.</p>
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<p><strong>Step 6:</strong>Since the dividend is less than the divisor, we need to add a<a>decimal</a>point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 2500.</p>
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<p><strong>Step 6:</strong>Since the dividend is less than the divisor, we need to add a<a>decimal</a>point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 2500.</p>
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<p><strong>Step 7:</strong>Now we need to find the new divisor, which is 705 because 705 x 3 = 2115.</p>
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<p><strong>Step 7:</strong>Now we need to find the new divisor, which is 705 because 705 x 3 = 2115.</p>
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<p><strong>Step 8:</strong>Subtracting 2115 from 2500, we get the result 385.</p>
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<p><strong>Step 8:</strong>Subtracting 2115 from 2500, we get the result 385.</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 √1250 is approximately 35.36.</p>
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<p>So the square root of √1250 is approximately 35.36.</p>
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<h2>Square Root of 1250 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 1250 using the approximation method.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √1250. The smallest perfect square of 1250 is 1225, and the largest perfect square of 1250 is 1296. √1250 falls somewhere between 35 and 36.</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 (1250 - 1225) ÷ (1296 - 1225) = 0.36. Using the formula, we identified the decimal point of our square root. The next step is adding the value we got initially to the decimal number, which is 35 + 0.36 = 35.36, so the square root of 1250 is approximately 35.36.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 1250</h2>
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<p>Students do make mistakes while finding the square root, like 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 √1250?</p>
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<p>Okay, lets begin</p>
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<p>The area of the square is 1250 square units.</p>
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<h3>Explanation</h3>
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<p>The area of the square = side^2.</p>
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<p>The side length is given as √1250.</p>
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<p>Area of the square = side^2 = √1250 x √1250 = 1250.</p>
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<p>Therefore, the area of the square box is 1250 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 1250 square feet is built; if each of the sides is √1250, 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>625 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 1250 by 2 = we get 625.</p>
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<p>So half of the building measures 625 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 √1250 x 4.</p>
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<p>Okay, lets begin</p>
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<p>141.42</p>
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<h3>Explanation</h3>
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<p>The first step is to find the square root of 1250, which is approximately 35.36.</p>
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<p>The second step is to multiply 35.36 by 4.</p>
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<p>So 35.36 x 4 = 141.42.</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 (1225 + 25)?</p>
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<p>Okay, lets begin</p>
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<p>The square root is 35.</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 (1225 + 25).</p>
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<p>1225 + 25 = 1250, and then √1250 ≈ 35.36.</p>
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<p>Therefore, the square root of (1225 + 25) is approximately 35.36.</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 √1250 units and the width ‘w’ is 30 units.</p>
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<p>Okay, lets begin</p>
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<p>We find the perimeter of the rectangle as 140.71 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 × (√1250 + 30)</p>
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<p>= 2 × (35.36 + 30)</p>
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<p>= 2 × 65.36</p>
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<p>= 130.71 units.</p>
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<p>Well explained 👍</p>
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<h2>FAQ on Square Root of 1250</h2>
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<h3>1.What is √1250 in its simplest form?</h3>
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<p>The prime factorization of 1250 is 2 x 5 x 5 x 5 x 5, so the simplest form of √1250 = √(2 x 5^4).</p>
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<h3>2.Mention the factors of 1250.</h3>
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<p>Factors of 1250 are 1, 2, 5, 10, 25, 50, 125, 250, 625, and 1250.</p>
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<h3>3.Calculate the square of 1250.</h3>
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<p>We get the square of 1250 by multiplying the number by itself, that is 1250 x 1250 = 1,562,500.</p>
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<h3>4.Is 1250 a prime number?</h3>
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<p>1250 is not a<a>prime number</a>, as it has more than two factors.</p>
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<h3>5.1250 is divisible by?</h3>
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<p>1250 has many factors; those are 1, 2, 5, 10, 25, 50, 125, 250, 625, and 1250.</p>
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<h2>Important Glossaries for the Square Root of 1250</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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<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 a principal square root. </li>
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<li><strong>Prime factorization:</strong>Prime factorization is expressing a number as the product of its prime factors. For example, the prime factorization of 18 is 2 x 3 x 3. </li>
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<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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<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>