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2026-01-01
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2026-02-28
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<p>247 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 242.</p>
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<h2>What is the Square Root of 242?</h2>
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<p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 242 is not a<a>perfect square</a>. The square root of 242 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √242, whereas (242)^(1/2) in the exponential form. √242 ≈ 15.5563, 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 242</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 242 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 242 is broken down into its prime factors.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 242 Breaking it down, we get 2 x 11 x 11: 2^1 x 11^2</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 242. The second step is to make pairs of those prime factors. Since 242 is not a perfect square, therefore the digits of the number can’t be grouped in perfect pairs. Therefore, calculating √242 using prime factorization directly is not feasible.</p>
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<h3>Explore Our Programs</h3>
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<h2>Square Root of 242 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 242, we need to group it as 42 and 2.</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 242, we need to group it as 42 and 2.</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 2. We can say n is '1' because 1 x 1 = 1, which is less than or equal to 2. Now the<a>quotient</a>is 1 and the<a>remainder</a>is 1 after subtracting 1 from 2.</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 2. We can say n is '1' because 1 x 1 = 1, which is less than or equal to 2. Now the<a>quotient</a>is 1 and the<a>remainder</a>is 1 after subtracting 1 from 2.</p>
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<p><strong>Step 3:</strong>Now let us bring down 42, making the new<a>dividend</a>142. Add the old<a>divisor</a>(1) with itself to get 2, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 42, making the new<a>dividend</a>142. Add the old<a>divisor</a>(1) with itself to get 2, which will be our new divisor.</p>
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<p><strong>Step 4:</strong>The new divisor will be 2n. We need to find the value of n.</p>
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<p><strong>Step 4:</strong>The new divisor will be 2n. We need to find the value of n.</p>
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<p><strong>Step 5:</strong>The next step is finding 2n x n ≤ 142. Let us consider n as 7, now 2 x 7 x 7 = 98.</p>
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<p><strong>Step 5:</strong>The next step is finding 2n x n ≤ 142. Let us consider n as 7, now 2 x 7 x 7 = 98.</p>
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<p><strong>Step 6:</strong>Subtract 98 from 142; the difference is 44, and the quotient is 17.</p>
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<p><strong>Step 6:</strong>Subtract 98 from 142; the difference is 44, and the quotient is 17.</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 4400.</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 4400.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 155 because 1553 x 3 = 4659.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 155 because 1553 x 3 = 4659.</p>
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<p><strong>Step 9:</strong>Subtracting 4659 from 4400, we get the result 241.</p>
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<p><strong>Step 9:</strong>Subtracting 4659 from 4400, we get the result 241.</p>
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<p><strong>Step 10:</strong>Now the quotient is 15.5.</p>
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<p><strong>Step 10:</strong>Now the quotient is 15.5.</p>
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<p><strong>Step 11:</strong>Continue doing these steps until we get two numbers after the decimal point or until the remainder is zero. So the square root of √242 is approximately 15.56.</p>
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<p><strong>Step 11:</strong>Continue doing these steps until we get two numbers after the decimal point or until the remainder is zero. So the square root of √242 is approximately 15.56.</p>
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<h2>Square Root of 242 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 242 using the approximation method.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √242. The closest perfect squares to 242 are 225 (15^2) and 256 (16^2). √242 falls somewhere between 15 and 16.</p>
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<p><strong>Step 2:</strong>Now we need to apply the<a>formula</a>that is (Given number - smaller perfect square) / (Larger perfect square - smaller perfect square). Using the formula (242 - 225) / (256 - 225) = 17/31 ≈ 0.5484. 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 integer part, which is 15 + 0.5484 ≈ 15.55, so the square root of 242 is approximately 15.55.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 242</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 √198?</p>
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<p>Okay, lets begin</p>
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<p>The area of the square is 198 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 √198.</p>
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<p>Area of the square = side^2 = √198 x √198 = 198.</p>
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<p>Therefore, the area of the square box is 198 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 242 square feet is built; if each of the sides is √242, 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>121 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 242 by 2, we get 121.</p>
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<p>So half of the building measures 121 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 √242 x 5.</p>
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<p>Okay, lets begin</p>
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<p>77.78</p>
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<h3>Explanation</h3>
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<p>The first step is to find the square root of 242, which is approximately 15.56.</p>
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<p>The second step is to multiply 15.56 by 5.</p>
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<p>So 15.56 x 5 ≈ 77.78.</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 (198 + 44)?</p>
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<p>Okay, lets begin</p>
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<p>The square root is 16.</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 (198 + 44).</p>
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<p>198 + 44 = 242, and then √242 ≈ 15.56.</p>
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<p>Therefore, the square root of (198 + 44) is approximately ±15.56.</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 √198 units and the width ‘w’ is 44 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 111.78 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 × (√198 + 44)</p>
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<p>= 2 × (14.07 + 44)</p>
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<p>= 2 × 58.07</p>
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<p>≈ 116.14 units.</p>
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<p>Well explained 👍</p>
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<h2>FAQ on Square Root of 242</h2>
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<h3>1.What is √242 in its simplest form?</h3>
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<p>The prime factorization of 242 is 2 x 11 x 11, so the simplest form of √242 = √(2 x 11^2) = 11√2.</p>
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<h3>2.Mention the factors of 242.</h3>
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<p>Factors of 242 are 1, 2, 11, 22, 121, and 242.</p>
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<h3>3.Calculate the square of 242.</h3>
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<p>We get the square of 242 by multiplying the number by itself, that is 242 x 242 = 58564.</p>
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<h3>4.Is 242 a prime number?</h3>
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<h3>5.242 is divisible by?</h3>
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<p>242 has<a>multiple</a>factors; it is divisible by 1, 2, 11, 22, 121, and 242.</p>
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<h2>Important Glossaries for the Square Root of 242</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, the positive square root is often used, known as the principal square root. </li>
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<li><strong>Prime Factorization:</strong>Breaking down a composite number into a product of its prime factors. For example, 242 = 2 x 11 x 11. </li>
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<li><strong>Long Division Method:</strong>A method to find the square root of non-perfect squares by dividing the number into groups and iteratively finding digits of the square root.</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>