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2026-01-01
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2026-02-28
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<p>321 Learners</p>
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<p>Last updated on<strong>August 5, 2025</strong></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 fields of vehicle design, finance, etc. Here, we will discuss the square root of 240.</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 fields of vehicle design, finance, etc. Here, we will discuss the square root of 240.</p>
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<h2>What is the Square Root of 240?</h2>
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<h2>What is the Square Root of 240?</h2>
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<p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 240 is not a<a>perfect square</a>. The square root of 240 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √240, whereas (240)^(1/2) in the exponential form. √240 ≈ 15.49193, 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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<p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 240 is not a<a>perfect square</a>. The square root of 240 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √240, whereas (240)^(1/2) in the exponential form. √240 ≈ 15.49193, 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 240</h2>
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<h2>Finding the Square Root of 240</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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<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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<ul><li>Prime factorization method</li>
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<li>Long division method</li>
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<li>Long division method</li>
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<li>Approximation method</li>
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<li>Approximation method</li>
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</ul><h2>Square Root of 240 by Prime Factorization Method</h2>
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</ul><h2>Square Root of 240 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 240 is broken down into its prime factors.</p>
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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 240 is broken down into its prime factors.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 240 Breaking it down, we get 2 × 2 × 2 × 2 × 3 × 5: 2^4 × 3 × 5</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 240 Breaking it down, we get 2 × 2 × 2 × 2 × 3 × 5: 2^4 × 3 × 5</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 240. The second step is to make pairs of those prime factors. Since 240 is not a perfect square, therefore the digits of the number can’t be grouped in pairs. Therefore, calculating √240 using prime factorization does not yield a<a>whole number</a>.</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 240. The second step is to make pairs of those prime factors. Since 240 is not a perfect square, therefore the digits of the number can’t be grouped in pairs. Therefore, calculating √240 using prime factorization does not yield a<a>whole number</a>.</p>
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<h2>Square Root of 240 by Long Division Method</h2>
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<h2>Square Root of 240 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 240, we need to group it as 40 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 240, we need to group it as 40 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 40 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 40 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 ≤ 140. Let us consider n as 7, now 2 × 7 × 7 = 98</p>
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<p><strong>Step 5:</strong>The next step is finding 2n × n ≤ 140. Let us consider n as 7, now 2 × 7 × 7 = 98</p>
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<p><strong>Step 6:</strong>Subtract 98 from 140, the difference is 42, and the quotient is 17</p>
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<p><strong>Step 6:</strong>Subtract 98 from 140, the difference is 42, 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 4200.</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 4200.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 154 because 154 × 27 = 4158</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 154 because 154 × 27 = 4158</p>
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<p><strong>Step 9:</strong>Subtracting 4158 from 4200 we get the result 42.</p>
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<p><strong>Step 9:</strong>Subtracting 4158 from 4200 we get the result 42.</p>
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<p><strong>Step 10:</strong>Now the quotient is 15.49</p>
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<p><strong>Step 10:</strong>Now the quotient is 15.49</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 √240 ≈ 15.49</p>
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<p>So the square root of √240 ≈ 15.49</p>
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<h2>Square Root of 240 by Approximation Method</h2>
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<h2>Square Root of 240 by Approximation Method</h2>
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<p>Approximation method is another method for finding the 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 240 using the approximation method.</p>
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<p>Approximation method is another method for finding the 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 240 using the approximation method.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √240 The smallest perfect square below 240 is 225 and the largest perfect square above 240 is 256. √240 falls somewhere between 15 and 16.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √240 The smallest perfect square below 240 is 225 and the largest perfect square above 240 is 256. √240 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 - smallest perfect square) / (Greater perfect square - smallest perfect square) Going by the formula (240 - 225) / (256 - 225) = 0.484 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 15 + 0.484 ≈ 15.484,</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 (240 - 225) / (256 - 225) = 0.484 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 15 + 0.484 ≈ 15.484,</p>
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<p>so the square root of 240 is approximately 15.49.</p>
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<p>so the square root of 240 is approximately 15.49.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 240</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 240</h2>
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<p>Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in 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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<p>Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in 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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<h2>Download Worksheets</h2>
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<h3>Problem 1</h3>
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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 √240?</p>
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<p>Can you help Max find the area of a square box if its side length is given as √240?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The area of the square box is 240 square units.</p>
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<p>The area of the square box is 240 square units.</p>
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<h3>Explanation</h3>
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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 area of the square = side².</p>
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<p>The side length is given as √240.</p>
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<p>The side length is given as √240.</p>
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<p>Area of the square = side² = √240 × √240 = 240.</p>
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<p>Area of the square = side² = √240 × √240 = 240.</p>
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<p>Therefore, the area of the square box is 240 square units.</p>
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<p>Therefore, the area of the square box is 240 square units.</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 2</h3>
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<h3>Problem 2</h3>
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<p>A square-shaped building measuring 240 square feet is built; if each of the sides is √240, what will be the square feet of half of the building?</p>
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<p>A square-shaped building measuring 240 square feet is built; if each of the sides is √240, 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>Okay, lets begin</p>
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<p>120 square feet</p>
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<p>120 square feet</p>
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<h3>Explanation</h3>
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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>We can just divide the given area by 2 as the building is square-shaped.</p>
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<p>Dividing 240 by 2 = we get 120.</p>
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<p>Dividing 240 by 2 = we get 120.</p>
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<p>So half of the building measures 120 square feet.</p>
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<p>So half of the building measures 120 square feet.</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 3</h3>
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<h3>Problem 3</h3>
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<p>Calculate √240 × 5.</p>
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<p>Calculate √240 × 5.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>Approximately 77.46</p>
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<p>Approximately 77.46</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>The first step is to find the square root of 240 which is approximately 15.49, the second step is to multiply 15.49 with 5.</p>
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<p>The first step is to find the square root of 240 which is approximately 15.49, the second step is to multiply 15.49 with 5.</p>
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<p>So 15.49 × 5 ≈ 77.46.</p>
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<p>So 15.49 × 5 ≈ 77.46.</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 4</h3>
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<h3>Problem 4</h3>
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<p>What will be the square root of (225 + 15)?</p>
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<p>What will be the square root of (225 + 15)?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The square root is approximately 15.49</p>
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<p>The square root is approximately 15.49</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>To find the square root, we need to find the sum of (225 + 15). 225 + 15 = 240, and then √240 ≈ 15.49.</p>
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<p>To find the square root, we need to find the sum of (225 + 15). 225 + 15 = 240, and then √240 ≈ 15.49.</p>
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<p>Therefore, the square root of (225 + 15) is approximately ±15.49.</p>
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<p>Therefore, the square root of (225 + 15) is approximately ±15.49.</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 5</h3>
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<h3>Problem 5</h3>
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<p>Find the perimeter of the rectangle if its length ‘l’ is √240 units and the width ‘w’ is 40 units.</p>
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<p>Find the perimeter of the rectangle if its length ‘l’ is √240 units and the width ‘w’ is 40 units.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>We find the perimeter of the rectangle as approximately 110.98 units.</p>
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<p>We find the perimeter of the rectangle as approximately 110.98 units.</p>
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<h3>Explanation</h3>
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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 of the rectangle = 2 × (length + width)</p>
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<p>Perimeter = 2 × (√240 + 40)</p>
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<p>Perimeter = 2 × (√240 + 40)</p>
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<p>= 2 × (15.49 + 40)</p>
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<p>= 2 × (15.49 + 40)</p>
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<p>= 2 × 55.49</p>
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<p>= 2 × 55.49</p>
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<p>≈ 110.98 units.</p>
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<p>≈ 110.98 units.</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h2>FAQ on Square Root of 240</h2>
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<h2>FAQ on Square Root of 240</h2>
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<h3>1.What is √240 in its simplest form?</h3>
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<h3>1.What is √240 in its simplest form?</h3>
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<p>The prime factorization of 240 is 2 × 2 × 2 × 2 × 3 × 5, so the simplest form of √240 = √(2^4 × 3 × 5).</p>
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<p>The prime factorization of 240 is 2 × 2 × 2 × 2 × 3 × 5, so the simplest form of √240 = √(2^4 × 3 × 5).</p>
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<h3>2.Mention the factors of 240.</h3>
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<h3>2.Mention the factors of 240.</h3>
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<p>Factors of 240 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, and 240.</p>
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<p>Factors of 240 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, and 240.</p>
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<h3>3.Calculate the square of 240.</h3>
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<h3>3.Calculate the square of 240.</h3>
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<p>We get the square of 240 by multiplying the number by itself, that is 240 × 240 = 57600.</p>
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<p>We get the square of 240 by multiplying the number by itself, that is 240 × 240 = 57600.</p>
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<h3>4.Is 240 a prime number?</h3>
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<h3>4.Is 240 a prime number?</h3>
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<h3>5.240 is divisible by?</h3>
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<h3>5.240 is divisible by?</h3>
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<p>240 has many factors; those are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, and 240.</p>
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<p>240 has many factors; those are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, and 240.</p>
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<h2>Important Glossaries for the Square Root of 240</h2>
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<h2>Important Glossaries for the Square Root of 240</h2>
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<ul><li><strong>Square root: A</strong>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><li><strong>Square root: A</strong>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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<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>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. </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. </li>
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<li><strong>Long division method:</strong>A method used to find the square root of numbers that are not perfect squares by dividing and finding the quotient step by step. </li>
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<li><strong>Long division method:</strong>A method used to find the square root of numbers that are not perfect squares by dividing and finding the quotient step by step. </li>
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<li><strong>Approximation method:</strong>A method to estimate the square root by finding the closest perfect squares above and below the target number and using them to find an approximate value.</li>
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<li><strong>Approximation method:</strong>A method to estimate the square root by finding the closest perfect squares above and below the target number and using them to find an approximate value.</li>
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</ul><p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>
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</ul><p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>
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<h2>Jaskaran Singh Saluja</h2>
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<h2>Jaskaran Singh Saluja</h2>
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<h3>About the Author</h3>
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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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<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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<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>
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<p>: He loves to play the quiz with kids through algebra to make kids love it.</p>