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2026-01-01
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2026-02-28
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<p>197 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 such as vehicle design, finance, etc. Here, we will discuss the square root of 355.</p>
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<h2>What is the Square Root of 355?</h2>
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<p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 355 is not a<a>perfect square</a>. The square root of 355 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √355, whereas (355)^(1/2) in the exponential form. √355 ≈ 18.84144, 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 355</h2>
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<p>The<a>prime factorization</a>method is used for perfect square numbers. However, for non-perfect square numbers like 355, 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 355 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 355 is broken down into its prime factors.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 355 Breaking it down, we get 5 x 71: 5^1 x 71^1</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 355. Since 355 is not a perfect square, we cannot group the digits into pairs.</p>
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<p>Therefore, calculating 355 using prime factorization is not feasible.</p>
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<h3>Explore Our Programs</h3>
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<h2>Square Root of 355 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 355, we need to group it as 55 and 3.</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 355, we need to group it as 55 and 3.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is ≤ 3. We can say n as ‘1’ because 1 x 1 is<a>less than</a>or equal to 3. Now the<a>quotient</a>is 1 after subtracting 1 x 1 from 3 leaves a<a>remainder</a>of 2.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is ≤ 3. We can say n as ‘1’ because 1 x 1 is<a>less than</a>or equal to 3. Now the<a>quotient</a>is 1 after subtracting 1 x 1 from 3 leaves a<a>remainder</a>of 2.</p>
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<p><strong>Step 3:</strong>Now let us bring down 55, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 1 + 1 to get 2, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 55, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 1 + 1 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 such that 2n x n ≤ 255. Let us consider n as 8, so 28 x 8 = 224.</p>
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<p><strong>Step 4:</strong>The new divisor will be 2n. We need to find the value of n such that 2n x n ≤ 255. Let us consider n as 8, so 28 x 8 = 224.</p>
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<p><strong>Step 5:</strong>Subtract 224 from 255; the difference is 31, and the quotient is 18.</p>
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<p><strong>Step 5:</strong>Subtract 224 from 255; the difference is 31, and the quotient is 18.</p>
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<p><strong>Step 6:</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 3100.</p>
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<p><strong>Step 6:</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 3100.</p>
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<p><strong>Step 7:</strong>Now we need to find the new divisor, which is 189 because 189 x 9 = 1701.</p>
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<p><strong>Step 7:</strong>Now we need to find the new divisor, which is 189 because 189 x 9 = 1701.</p>
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<p><strong>Step 8:</strong>Subtracting 1701 from 3100 gives us the result 1399.</p>
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<p><strong>Step 8:</strong>Subtracting 1701 from 3100 gives us the result 1399.</p>
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<p><strong>Step 9:</strong>Now the quotient is 18.8.</p>
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<p><strong>Step 9:</strong>Now the quotient is 18.8.</p>
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<p><strong>Step 10:</strong>Continue doing these steps until we get two numbers after the decimal point. If there are no decimal values, continue until the remainder is zero.</p>
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<p><strong>Step 10:</strong>Continue doing these steps until we get two numbers after the decimal point. If there are no decimal values, continue until the remainder is zero.</p>
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<p>So the square root of √355 is approximately 18.84.</p>
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<p>So the square root of √355 is approximately 18.84.</p>
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<h2>Square Root of 355 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 355 using the approximation method.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect squares of √355.</p>
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<p>The smallest perfect square less than 355 is 324, and the largest perfect square<a>greater than</a>355 is 361. √355 falls somewhere between 18 and 19.</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 (355 - 324) / (361 - 324) = 31/37 ≈ 0.8378. 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 18 + 0.8378 ≈ 18.84, so the square root of 355 is approximately 18.84.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 355</h2>
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<p>Students do make mistakes while finding the square root, such as forgetting about the negative square root and skipping long division methods. 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 √355?</p>
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<p>Okay, lets begin</p>
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<p>The area of the square is 355 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 √355.</p>
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<p>Area of the square = side^2 = √355 x √355 = 355.</p>
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<p>Therefore, the area of the square box is 355 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 355 square feet is built; if each of the sides is √355, 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>177.5 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>355 by 2, we get 177.5.</p>
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<p>So half of the building measures 177.5 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 √355 x 5.</p>
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<p>Okay, lets begin</p>
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<p>94.2072</p>
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<h3>Explanation</h3>
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<p>The first step is to find the square root of 355, which is approximately 18.84.</p>
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<p>The second step is to multiply 18.84 with 5.</p>
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<p>So 18.84 x 5 = 94.2072.</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 (345 + 10)?</p>
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<p>Okay, lets begin</p>
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<p>The square root is 19.</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 (345 + 10). 345 + 10 = 355, and then √355 ≈ 18.84.</p>
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<p>Therefore, the square root of (345 + 10) is approximately 18.84.</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 √355 units and the width ‘w’ is 45 units.</p>
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<p>Okay, lets begin</p>
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<p>We find the perimeter of the rectangle as 127.68 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 × (√355 + 45) = 2 × (18.84 + 45) = 2 × 63.84 = 127.68 units.</p>
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<p>Well explained 👍</p>
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<h2>FAQ on Square Root of 355</h2>
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<h3>1.What is √355 in its simplest form?</h3>
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<p>The prime factorization of 355 is 5 x 71, so the simplest form of √355 = √(5 x 71).</p>
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<h3>2.Mention the factors of 355.</h3>
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<p>Factors of 355 are 1, 5, 71, and 355.</p>
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<h3>3.Calculate the square of 355.</h3>
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<p>We get the square of 355 by multiplying the number by itself, that is 355 x 355 = 126025.</p>
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<h3>4.Is 355 a prime number?</h3>
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<h3>5.355 is divisible by?</h3>
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<p>355 has several factors; those are 1, 5, 71, and 355.</p>
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<h2>Important Glossaries for the Square Root of 355</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, which 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 representing a number as a product of its prime factors.</li>
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</ul><ul><li><strong>Decimal:</strong>A decimal number is a number that has a whole number and a fraction part, separated by a decimal point, such as 7.86, 8.65, and 9.42.</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>