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2026-01-01
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2026-02-28
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<p>207 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 itself, the result is a square. The inverse of the square is a square root. The square root is used in the fields of vehicle design, finance, etc. Here, we will discuss the square root of 340.</p>
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<h2>What is the Square Root of 340?</h2>
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<p>The<a>square</a>root is the inverse of squaring a<a>number</a>. 340 is not a<a>perfect square</a>. The square root of 340 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √340, whereas (340)^(1/2) in the exponential form. √340 ≈ 18.43909, 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 340</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 340 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 340 is broken down into its prime factors.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 340 Breaking it down, we get 2 x 2 x 5 x 17: 2² x 5¹ x 17¹</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 340. The second step is to make pairs of those prime factors. Since 340 is not a perfect square, the digits of the number can’t be grouped into pairs.</p>
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<p>Therefore, calculating the<a>square root</a>of 340 using prime factorization is not straightforward.</p>
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<h3>Explore Our Programs</h3>
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<h2>Square Root of 340 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 340, we need to group it as 40 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 340, we need to group it as 40 and 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 3. We can say n is ‘1’ because 1 x 1 is lesser than or equal to 3. Now the<a>quotient</a>is 1. After subtracting 1 x 1 from 3, the<a>remainder</a>is 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 3. We can say n is ‘1’ because 1 x 1 is lesser than or equal to 3. Now the<a>quotient</a>is 1. After subtracting 1 x 1 from 3, the<a>remainder</a>is 2.</p>
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<p><strong>Step 3:</strong>Now let us bring down 40, making the new<a>dividend</a>240. 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 40, making the new<a>dividend</a>240. 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 ≤ 240. Let us consider n as 8. Now 28 x 8 = 224.</p>
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<p><strong>Step 5:</strong>The next step is finding 2n × n ≤ 240. Let us consider n as 8. Now 28 x 8 = 224.</p>
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<p><strong>Step 6:</strong>Subtract 224 from 240; the difference is 16, and the quotient is 18.</p>
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<p><strong>Step 6:</strong>Subtract 224 from 240; the difference is 16, and the quotient is 18.</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 1600.</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 1600.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor. We choose 184 because 184 x 4 = 736.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor. We choose 184 because 184 x 4 = 736.</p>
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<p><strong>Step 9:</strong>Subtracting 736 from 1600, we get the result 864.</p>
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<p><strong>Step 9:</strong>Subtracting 736 from 1600, we get the result 864.</p>
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<p><strong>Step 10:</strong>Now the quotient is 18.4</p>
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<p><strong>Step 10:</strong>Now the quotient is 18.4</p>
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<p><strong>Step 11:</strong>Continue doing these steps until we get two numbers after the decimal point. Suppose there are no decimal values; continue until 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 there are no decimal values; continue until the remainder is zero.</p>
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<p>So the square root of √340 is approximately 18.439.</p>
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<p>So the square root of √340 is approximately 18.439.</p>
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<h2>Square Root of 340 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 340 using the approximation method.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect squares to √340.</p>
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<p>The smallest perfect square less than 340 is 324, and the largest perfect square<a>greater than</a>340 is 361. √340 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>: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Going by the formula: (340 - 324) / (361 - 324) = 16 / 37 ≈ 0.432.</p>
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<p>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 + 0.432 ≈ 18.432; so the square root of 340 is approximately 18.432.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 340</h2>
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<p>Students 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 √340?</p>
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<p>Okay, lets begin</p>
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<p>The area of the square is approximately 1153.792 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 √340.</p>
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<p>Area of the square = side² = √340 x √340 ≈ 18.439 x 18.439 ≈ 1153.792.</p>
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<p>Therefore, the area of the square box is approximately 1153.792 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 340 square feet is built; if each of the sides is √340, 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>170 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 340 by 2, we get 170.</p>
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<p>So, half of the building measures 170 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 √340 x 5.</p>
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<p>Okay, lets begin</p>
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<p>Approximately 92.195</p>
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<h3>Explanation</h3>
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<p>The first step is to find the square root of 340, which is approximately 18.439.</p>
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<p>The second step is to multiply 18.439 by 5.</p>
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<p>So, 18.439 x 5 ≈ 92.195.</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 (324 + 16)?</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 (324 + 16). 324 + 16 = 340, and then √340 ≈ 18.439.</p>
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<p>Therefore, the square root of (324 + 16) is ±18.439.</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 √340 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 112.878 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 × (√340 + 38) ≈ 2 × (18.439 + 38) ≈ 2 × 56.439 ≈ 112.878 units.</p>
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<p>Well explained 👍</p>
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<h2>FAQ on Square Root of 340</h2>
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<h3>1.What is √340 in its simplest form?</h3>
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<p>The prime factorization of 340 is 2 x 2 x 5 x 17, so the simplest form of √340 = √(2² x 5 x 17).</p>
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<h3>2.Mention the factors of 340.</h3>
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<p>Factors of 340 are 1, 2, 4, 5, 10, 17, 20, 34, 68, 85, 170, and 340.</p>
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<h3>3.Calculate the square of 340.</h3>
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<p>We get the square of 340 by multiplying the number by itself, that is 340 x 340 = 115,600.</p>
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<h3>4.Is 340 a prime number?</h3>
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<h3>5.340 is divisible by?</h3>
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<p>340 has many factors; those are 1, 2, 4, 5, 10, 17, 20, 34, 68, 85, 170, and 340.</p>
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<h2>Important Glossaries for the Square Root of 340</h2>
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<ul><li><strong>Square root:</strong>A square root is the inverse of squaring a number. Example: 4² = 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>Integer:</strong>An integer is any whole number, positive or negative, including zero. For example, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, etc., are integers.</li>
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</ul><ul><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>