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2026-01-01
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2026-02-28
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<p>185 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 like vehicle design, finance, etc. Here, we will discuss the square root of 270.</p>
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<h2>What is the Square Root of 270?</h2>
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<p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 270 is not a<a>perfect square</a>. The square root of 270 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √270, whereas (270)^(1/2) in the exponential form. √270 ≈ 16.43168, 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 270</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 270 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 270 is broken down into its prime factors.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 270</p>
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<p>Breaking it down, we get 2 × 3 × 3 × 3 × 5: 2^1 × 3^3 × 5^1</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 270. The second step is to make pairs of those prime factors. Since 270 is not a perfect square, therefore the digits of the number can’t be grouped in pairs. Therefore, calculating 270 using prime factorization is impossible.</p>
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<h3>Explore Our Programs</h3>
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<h2>Square Root of 270 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 270, we need to group it as 70 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 270, we need to group it as 70 and 2.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is 2. We can say n as ‘1’ because 1 × 1 is lesser than or equal to 2. Now the<a>quotient</a>is 1; after subtracting 1 from 2, the<a>remainder</a>is 1.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is 2. We can say n as ‘1’ because 1 × 1 is lesser than or equal to 2. Now the<a>quotient</a>is 1; after subtracting 1 from 2, the<a>remainder</a>is 1.</p>
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<p><strong>Step 3:</strong>Now let us bring down 70, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number, 1 + 1, we get 2, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 70, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number, 1 + 1, we get 2, 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 2n 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 2n 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 2n × n ≤ 170. Let us consider n as 6; now 2 × 6 × 6 = 72.</p>
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<p><strong>Step 5:</strong>The next step is finding 2n × n ≤ 170. Let us consider n as 6; now 2 × 6 × 6 = 72.</p>
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<p><strong>Step 6:</strong>Subtract 72 from 170; the difference is 98, and the quotient is 16.</p>
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<p><strong>Step 6:</strong>Subtract 72 from 170; the difference is 98, and the quotient is 16.</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 9800.</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 9800.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 164 because 164 × 4 = 656.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 164 because 164 × 4 = 656.</p>
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<p><strong>Step 9:</strong>Subtracting 656 from 9800, we get the result 3144.</p>
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<p><strong>Step 9:</strong>Subtracting 656 from 9800, we get the result 3144.</p>
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<p><strong>Step 10:</strong>Now the quotient is 16.4.</p>
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<p><strong>Step 10:</strong>Now the quotient is 16.4.</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 are 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 are no decimal values, continue till the remainder is zero.</p>
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<p>So the square root of √270 is approximately 16.43.</p>
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<p>So the square root of √270 is approximately 16.43.</p>
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<h2>Square Root of 270 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 270 using the approximation method.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √270. The smallest perfect square<a>less than</a>270 is 256, and the largest perfect square<a>greater than</a>270 is 289. √270 falls somewhere between 16 and 17.</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 (270 - 256) / (289 - 256) = 14 / 33 ≈ 0.42. 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 16 + 0.42 = 16.42, so the square root of 270 is approximately 16.42.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 270</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 √245?</p>
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<p>Okay, lets begin</p>
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<p>The area of the square is approximately 245 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 √245.</p>
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<p>Area of the square = side^2 = √245 × √245 = 245.</p>
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<p>Therefore, the area of the square box is approximately 245 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 270 square feet is built; if each of the sides is √270, 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>135 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 270 by 2, we get 135.</p>
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<p>So, half of the building measures 135 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 √270 × 5.</p>
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<p>Okay, lets begin</p>
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<p>Approximately 82.16</p>
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<h3>Explanation</h3>
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<p>The first step is to find the square root of 270, which is approximately 16.43.</p>
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<p>The second step is to multiply 16.43 by 5.</p>
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<p>So, 16.43 × 5 ≈ 82.16.</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 (245 + 25)?</p>
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<p>Okay, lets begin</p>
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<p>The square root is approximately 17.</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 (245 + 25). 245 + 25 = 270, and then √270 is approximately 16.43.</p>
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<p>Therefore, the square root of (245 + 25) is approximately ±16.43.</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 √245 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 approximately 115.43 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 × (√245 + 38) ≈ 2 × (15.65 + 38) = 2 × 53.65 ≈ 107.3 units.</p>
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<p>Well explained 👍</p>
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<h2>FAQ on Square Root of 270</h2>
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<h3>1.What is √270 in its simplest form?</h3>
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<p>The prime factorization of 270 is 2 × 3 × 3 × 3 × 5, so the simplest form of √270 ≈ √(2 × 3^3 × 5).</p>
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<h3>2.Mention the factors of 270.</h3>
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<p>Factors of 270 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, and 270.</p>
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<h3>3.Calculate the square of 270.</h3>
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<p>We get the square of 270 by multiplying the number by itself, that is 270 × 270 = 72900.</p>
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<h3>4.Is 270 a prime number?</h3>
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<h3>5.270 is divisible by?</h3>
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<p>270 has many factors; those are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, and 270.</p>
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<h2>Important Glossaries for the Square Root of 270</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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</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 the principal square root.</li>
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</ul><ul><li><strong>Prime factorization:</strong>The process of expressing a number as the product of its prime factors. For example, 270 = 2 × 3 × 3 × 3 × 5.</li>
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</ul><ul><li><strong>Decimal approximation:</strong>A method to estimate the value of an irrational number using decimals. For example, √270 ≈ 16.43.</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>