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2026-01-01
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2026-02-28
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<p>229 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 1240.</p>
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<h2>What is the Square Root of 1240?</h2>
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<p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 1240 is not a<a>perfect square</a>. The square root of 1240 is expressed in both radical and<a>exponential form</a>. In radical form, it is expressed as √1240, whereas (1240)^(1/2) in exponential form. √1240 ≈ 35.2136, 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 1240</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 1240 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 1240 is broken down into its prime factors.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 1240 Breaking it down, we get 2 × 2 × 2 × 5 × 31: 2^3 × 5^1 × 31^1</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 1240. The second step is to make pairs of those prime factors. Since 1240 is not a perfect square, the digits of the number can’t be grouped in pairs.</p>
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<p>Therefore, calculating 1240 using prime factorization is not possible to yield a perfect<a>square root</a>.</p>
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<h3>Explore Our Programs</h3>
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<h2>Square Root of 1240 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 1240, we need to group it as 40 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 1240, we need to group it as 40 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 × 3 = 9 is less than 12. Now the<a>quotient</a>is 3, after subtracting 12 - 9, 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 × 3 = 9 is less than 12. Now the<a>quotient</a>is 3, after subtracting 12 - 9, the<a>remainder</a>is 3.</p>
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<p><strong>Step 3:</strong>Now let us bring down 40, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 3 + 3, we get 6, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 40, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 3 + 3, we get 6, which will be our new divisor.</p>
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<p><strong>Step 4:</strong>The new divisor will be 6n. Now, find the value of n.</p>
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<p><strong>Step 4:</strong>The new divisor will be 6n. Now, find the value of n.</p>
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<p><strong>Step 5:</strong>The next step is finding 6n × n ≤ 340. Let us consider n as 5, now 65 × 5 = 325.</p>
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<p><strong>Step 5:</strong>The next step is finding 6n × n ≤ 340. Let us consider n as 5, now 65 × 5 = 325.</p>
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<p><strong>Step 6:</strong>Subtract 340 from 325; the difference is 15, and the quotient is 35.</p>
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<p><strong>Step 6:</strong>Subtract 340 from 325; the difference is 15, and the quotient is 35.</p>
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<p><strong>Step 7:</strong>Since the remainder is less than the divisor, we need to add a<a>decimal</a>point. Adding the decimal point allows us to bring down pairs of zeros. Now the new dividend is 1500.</p>
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<p><strong>Step 7:</strong>Since the remainder is less than the divisor, we need to add a<a>decimal</a>point. Adding the decimal point allows us to bring down pairs of zeros. Now the new dividend is 1500.</p>
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<p><strong>Step 8:</strong>Now we need to find the next digit for the divisor. Consider 705 × 2 = 1410.</p>
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<p><strong>Step 8:</strong>Now we need to find the next digit for the divisor. Consider 705 × 2 = 1410.</p>
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<p><strong>Step 9:</strong>Subtracting 1410 from 1500, we get the result 90.</p>
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<p><strong>Step 9:</strong>Subtracting 1410 from 1500, we get the result 90.</p>
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<p><strong>Step 10:</strong>Now the quotient is 35.2.</p>
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<p><strong>Step 10:</strong>Now the quotient is 35.2.</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 √1240 is approximately 35.21.</p>
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<p>So the square root of √1240 is approximately 35.21.</p>
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<h2>Square Root of 1240 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 1240 using the approximation method.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √1240. The smallest perfect square less than 1240 is 1225, and the largest perfect square<a>greater than</a>1240 is 1296. √1240 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>that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Going by the formula (1240 - 1225) ÷ (1296 - 1225) = 15 ÷ 71 ≈ 0.2113 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 + 0.2113 ≈ 35.2113, so the square root of 1240 is approximately 35.21.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 1240</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 √1240?</p>
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<p>Okay, lets begin</p>
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<p>The area of the square is approximately 1240 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 √1240.</p>
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<p>Area of the square = side² = √1240 x √1240 = 1240.</p>
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<p>Therefore, the area of the square box is approximately 1240 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 1240 square feet is built; if each of the sides is √1240, 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>620 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 1240 by 2, we get 620.</p>
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<p>So half of the building measures 620 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 √1240 × 5.</p>
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<p>Okay, lets begin</p>
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<p>176.07</p>
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<h3>Explanation</h3>
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<p>The first step is to find the square root of 1240, which is approximately 35.21.</p>
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<p>The second step is to multiply 35.21 with 5.</p>
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<p>So 35.21 × 5 ≈ 176.07.</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 + 15)?</p>
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<p>Okay, lets begin</p>
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<p>The square root is approximately 35.21.</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 + 15).</p>
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<p>1225 + 15 = 1240, and then √1240 ≈ 35.21.</p>
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<p>Therefore, the square root of (1225 + 15) is approximately ±35.21.</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 √1240 units and the width ‘w’ is 40 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 150.42 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 × (√1240 + 40)</p>
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<p>≈ 2 × (35.21 + 40)</p>
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<p>≈ 2 × 75.21</p>
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<p>≈ 150.42 units.</p>
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<p>Well explained 👍</p>
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<h2>FAQ on Square Root of 1240</h2>
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<h3>1.What is √1240 in its simplest form?</h3>
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<p>The prime factorization of 1240 is 2 × 2 × 2 × 5 × 31, so the simplest form of √1240 = √(2 × 2 × 2 × 5 × 31).</p>
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<h3>2.Mention the factors of 1240.</h3>
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<p>Factors of 1240 are 1, 2, 4, 5, 8, 10, 20, 31, 40, 62, 124, 155, 248, 310, 620, and 1240.</p>
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<h3>3.Calculate the square of 1240.</h3>
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<p>We get the square of 1240 by multiplying the number by itself, that is 1240 × 1240 = 1,537,600.</p>
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<h3>4.Is 1240 a prime number?</h3>
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<p>1240 is not a<a>prime number</a>, as it has more than two factors.</p>
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<h3>5.1240 is divisible by?</h3>
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<p>1240 has many factors; those are 1, 2, 4, 5, 8, 10, 20, 31, 40, 62, 124, 155, 248, 310, 620, and 1240.</p>
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<h2>Important Glossaries for the Square Root of 1240</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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<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>It is the process of expressing a number as the product of its prime factors. For example, the prime factorization of 1240 is 2 × 2 × 2 × 5 × 31. </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>