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2026-01-01
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2026-02-28
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<p>237 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 itself, 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 216.</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 fields such as vehicle design, finance, etc. Here, we will discuss the square root of 216.</p>
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<h2>What is the Square Root of 216?</h2>
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<h2>What is the Square Root of 216?</h2>
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<p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 216 is not a<a>perfect square</a>. The square root of 216 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √216, whereas (216)^(1/2) in the exponential form. √216 ≈ 14.69694, 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>. 216 is not a<a>perfect square</a>. The square root of 216 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √216, whereas (216)^(1/2) in the exponential form. √216 ≈ 14.69694, 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 216</h2>
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<h2>Finding the Square Root of 216</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 216 by Prime Factorization Method</h2>
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</ul><h2>Square Root of 216 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 216 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 216 is broken down into its prime factors.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 216 Breaking it down, we get 2 x 2 x 2 x 3 x 3 x 3: 2^3 x 3^3</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 216 Breaking it down, we get 2 x 2 x 2 x 3 x 3 x 3: 2^3 x 3^3</p>
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<p><strong>Step 2:</strong>Now we found the prime factors of 216. The second step is to make pairs of those prime factors. Since 216 is not a perfect square, the digits of the number can’t be grouped in pairs.</p>
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<p><strong>Step 2:</strong>Now we found the prime factors of 216. The second step is to make pairs of those prime factors. Since 216 is not a perfect square, the digits of the number can’t be grouped in pairs.</p>
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<p>Therefore, calculating 216 using prime factorization is impossible.</p>
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<p>Therefore, calculating 216 using prime factorization is impossible.</p>
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<h2>Square Root of 216 by Long Division Method</h2>
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<h2>Square Root of 216 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 216, we need to group it as 16 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 216, we need to group it as 16 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 x 1 is lesser than or equal to 2. Now the<a>quotient</a>is 1; after subtracting 1, 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 x 1 is lesser than or equal to 2. Now the<a>quotient</a>is 1; after subtracting 1, the<a>remainder</a>is 1.</p>
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<p><strong>Step 3:</strong>Now let us bring down 16, 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 16, 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 ≤ 116; let us consider n as 4; now 2 x 4 x 4 = 96.</p>
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<p><strong>Step 5:</strong>The next step is finding 2n × n ≤ 116; let us consider n as 4; now 2 x 4 x 4 = 96.</p>
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<p><strong>Step 6:</strong>Subtract 116 from 96; the difference is 20, and the quotient is 14.</p>
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<p><strong>Step 6:</strong>Subtract 116 from 96; the difference is 20, and the quotient is 14.</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 2000.</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 2000.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 146, because 1464 x 4 = 1964.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 146, because 1464 x 4 = 1964.</p>
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<p><strong>Step 9:</strong>Subtracting 1964 from 2000, we get the result 36.</p>
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<p><strong>Step 9:</strong>Subtracting 1964 from 2000, we get the result 36.</p>
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<p><strong>Step 10:</strong>Now the quotient is 14.6.</p>
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<p><strong>Step 10:</strong>Now the quotient is 14.6.</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 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 if there are no decimal values, continue until the remainder is zero.</p>
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<p>So the square root of √216 is approximately 14.69.</p>
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<p>So the square root of √216 is approximately 14.69.</p>
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<h2>Square Root of 216 by Approximation Method</h2>
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<h2>Square Root of 216 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 216 using the approximation method.</p>
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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 216 using the approximation method.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect squares to √216. The smallest perfect square<a>less than</a>216 is 196, and the largest perfect square<a>greater than</a>216 is 225. √216 falls somewhere between 14 and 15.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect squares to √216. The smallest perfect square<a>less than</a>216 is 196, and the largest perfect square<a>greater than</a>216 is 225. √216 falls somewhere between 14 and 15.</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, (216 - 196) ÷ (225 - 196) = 20 ÷ 29 ≈ 0.6897. 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 14 + 0.69 ≈ 14.69, so the square root of 216 is approximately 14.69.</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, (216 - 196) ÷ (225 - 196) = 20 ÷ 29 ≈ 0.6897. 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 14 + 0.69 ≈ 14.69, so the square root of 216 is approximately 14.69.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 216</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 216</h2>
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<p>Students do make mistakes while finding the square root, like forgetting about the negative square root or skipping long division steps, etc. 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, like forgetting about the negative square root or skipping long division steps, etc. 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 √216?</p>
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<p>Can you help Max find the area of a square box if its side length is given as √216?</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 is approximately 216 square units.</p>
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<p>The area of the square is approximately 216 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 = side^2.</p>
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<p>The area of the square = side^2.</p>
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<p>The side length is given as √216.</p>
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<p>The side length is given as √216.</p>
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<p>Area of the square = (√216) x (√216) = 14.69 × 14.69 ≈ 216.</p>
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<p>Area of the square = (√216) x (√216) = 14.69 × 14.69 ≈ 216.</p>
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<p>Therefore, the area of the square box is approximately 216 square units.</p>
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<p>Therefore, the area of the square box is approximately 216 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 216 square feet is built; if each of the sides is √216, what will be the square feet of half of the building?</p>
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<p>A square-shaped building measuring 216 square feet is built; if each of the sides is √216, 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>108 square feet</p>
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<p>108 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 216 by 2 = we get 108.</p>
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<p>Dividing 216 by 2 = we get 108.</p>
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<p>So half of the building measures 108 square feet.</p>
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<p>So half of the building measures 108 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 √216 × 4.</p>
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<p>Calculate √216 × 4.</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 58.79</p>
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<p>Approximately 58.79</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 216, which is approximately 14.69.</p>
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<p>The first step is to find the square root of 216, which is approximately 14.69.</p>
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<p>The second step is to multiply 14.69 by 4. So 14.69 × 4 ≈ 58.79.</p>
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<p>The second step is to multiply 14.69 by 4. So 14.69 × 4 ≈ 58.79.</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 (200 + 16)?</p>
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<p>What will be the square root of (200 + 16)?</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 14.69.</p>
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<p>The square root is approximately 14.69.</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 (200 + 16).</p>
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<p>To find the square root, we need to find the sum of (200 + 16).</p>
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<p>200 + 16 = 216, and then √216 ≈ 14.69.</p>
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<p>200 + 16 = 216, and then √216 ≈ 14.69.</p>
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<p>Therefore, the square root of (200 + 16) is approximately ±14.69.</p>
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<p>Therefore, the square root of (200 + 16) is approximately ±14.69.</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 √216 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 √216 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>The perimeter of the rectangle is approximately 109.38 units.</p>
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<p>The perimeter of the rectangle is approximately 109.38 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 × (√216 + 40) = 2 × (14.69 + 40) = 2 × 54.69 ≈ 109.38 units.</p>
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<p>Perimeter = 2 × (√216 + 40) = 2 × (14.69 + 40) = 2 × 54.69 ≈ 109.38 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 216</h2>
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<h2>FAQ on Square Root of 216</h2>
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<h3>1.What is √216 in its simplest form?</h3>
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<h3>1.What is √216 in its simplest form?</h3>
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<p>The prime factorization of 216 is 2 x 2 x 2 x 3 x 3 x 3, so the simplest form of √216 is √(2^3 x 3^3).</p>
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<p>The prime factorization of 216 is 2 x 2 x 2 x 3 x 3 x 3, so the simplest form of √216 is √(2^3 x 3^3).</p>
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<h3>2.Mention the factors of 216.</h3>
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<h3>2.Mention the factors of 216.</h3>
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<p>Factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, and 216.</p>
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<p>Factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, and 216.</p>
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<h3>3.Calculate the square of 216.</h3>
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<h3>3.Calculate the square of 216.</h3>
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<p>We get the square of 216 by multiplying the number by itself, that is 216 x 216 = 46656.</p>
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<p>We get the square of 216 by multiplying the number by itself, that is 216 x 216 = 46656.</p>
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<h3>4.Is 216 a prime number?</h3>
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<h3>4.Is 216 a prime number?</h3>
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<h3>5.216 is divisible by?</h3>
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<h3>5.216 is divisible by?</h3>
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<p>216 has many factors; those are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, and 216.</p>
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<p>216 has many factors; those are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, and 216.</p>
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<h2>Important Glossaries for the Square Root of 216</h2>
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<h2>Important Glossaries for the Square Root of 216</h2>
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<ul><li><strong>Square root:</strong>A square root is the inverse of a square. For example: 4^2 = 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:</strong>A square root is the inverse of a square. For 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>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.<strong></strong></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.<strong></strong></li>
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</ul><ul><li><strong>Perfect square:</strong>A number that is the square of an integer. For example, 16 is a perfect square because it is 4^2.</li>
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</ul><ul><li><strong>Perfect square:</strong>A number that is the square of an integer. For example, 16 is a perfect square because it is 4^2.</li>
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</ul><ul><li><strong>Long division method:</strong>A method used to find the square root of non-perfect squares through a series of division steps.</li>
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</ul><ul><li><strong>Long division method:</strong>A method used to find the square root of non-perfect squares through a series of division steps.</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>