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2026-01-01
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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 field of vehicle design, finance, etc. Here, we will discuss the square root of 194.75.</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 field of vehicle design, finance, etc. Here, we will discuss the square root of 194.75.</p>
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<h2>What is the Square Root of 194.75?</h2>
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<h2>What is the Square Root of 194.75?</h2>
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<p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 194.75 is not a<a>perfect square</a>. The square root of 194.75 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √194.75, whereas (194.75)^(1/2) in the exponential form. √194.75 ≈ 13.954, 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>. 194.75 is not a<a>perfect square</a>. The square root of 194.75 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √194.75, whereas (194.75)^(1/2) in the exponential form. √194.75 ≈ 13.954, 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 194.75</h2>
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<h2>Finding the Square Root of 194.75</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>and approximation methods 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>and approximation methods 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 194.75 by Prime Factorization Method</h2>
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</ul><h2>Square Root of 194.75 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. Since 194.75 is not an integer, it does not have a straightforward prime factorization like<a>whole numbers</a>. Therefore, calculating 194.75 using prime factorization is not applicable.</p>
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<p>The<a>product</a>of prime<a>factors</a>is the prime factorization of a number. Since 194.75 is not an integer, it does not have a straightforward prime factorization like<a>whole numbers</a>. Therefore, calculating 194.75 using prime factorization is not applicable.</p>
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<h2>Square Root of 194.75 by Long Division Method</h2>
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<h2>Square Root of 194.75 by Long Division Method</h2>
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<p>The<a>long division</a>method is particularly used for non-perfect square numbers. 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. 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 pairs. In the case of 194.75, consider it as 19475 (ignoring the<a>decimal</a>for now).</p>
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<p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left in pairs. In the case of 194.75, consider it as 19475 (ignoring the<a>decimal</a>for now).</p>
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<p><strong>Step 2:</strong>Determine the largest number whose square is<a>less than</a>or equal to 1. Here, it is 1.</p>
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<p><strong>Step 2:</strong>Determine the largest number whose square is<a>less than</a>or equal to 1. Here, it is 1.</p>
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<p><strong>Step 3:</strong>Subtract 1 from 1 to get a<a>remainder</a>of 0 and bring down 94 to make it 94.</p>
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<p><strong>Step 3:</strong>Subtract 1 from 1 to get a<a>remainder</a>of 0 and bring down 94 to make it 94.</p>
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<p><strong>Step 4:</strong>Double the<a>divisor</a>(which is 1) to get 2, and find a number n such that 2n × n ≤ 94. Choose n = 4, as 24 × 4 = 96, which is<a>greater than</a>94. So, n = 3, giving us 23 × 3 = 69.</p>
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<p><strong>Step 4:</strong>Double the<a>divisor</a>(which is 1) to get 2, and find a number n such that 2n × n ≤ 94. Choose n = 4, as 24 × 4 = 96, which is<a>greater than</a>94. So, n = 3, giving us 23 × 3 = 69.</p>
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<p><strong>Step 5:</strong>Subtract 69 from 94 to get a remainder of 25. Bring down 75 to make it 2575.</p>
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<p><strong>Step 5:</strong>Subtract 69 from 94 to get a remainder of 25. Bring down 75 to make it 2575.</p>
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<p><strong>Step 6:</strong>Double the current quotient (13) to get 26, and find n such that 26n × n ≤ 2575. Choose n = 9, as 269 × 9 = 2421.</p>
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<p><strong>Step 6:</strong>Double the current quotient (13) to get 26, and find n such that 26n × n ≤ 2575. Choose n = 9, as 269 × 9 = 2421.</p>
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<p><strong>Step 7:</strong>Subtract 2421 from 2575 to get 154.</p>
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<p><strong>Step 7:</strong>Subtract 2421 from 2575 to get 154.</p>
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<p><strong>Step 8:</strong>Continue this process, adding zeros in pairs to the remainder and repeating steps to obtain more decimal places.</p>
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<p><strong>Step 8:</strong>Continue this process, adding zeros in pairs to the remainder and repeating steps to obtain more decimal places.</p>
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<p>The square root of 194.75 is approximately 13.954.</p>
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<p>The square root of 194.75 is approximately 13.954.</p>
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<h2>Square Root of 194.75 by Approximation Method</h2>
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<h2>Square Root of 194.75 by Approximation Method</h2>
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<p>The approximation method is another method for finding square roots, and 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 194.75 using the approximation method.</p>
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<p>The approximation method is another method for finding square roots, and 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 194.75 using the approximation method.</p>
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<p><strong>Step 1:</strong>Identify the closest perfect squares around 194.75. The smallest perfect square less than 194.75 is 169, and the largest perfect square greater than 194.75 is 225.</p>
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<p><strong>Step 1:</strong>Identify the closest perfect squares around 194.75. The smallest perfect square less than 194.75 is 169, and the largest perfect square greater than 194.75 is 225.</p>
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<p><strong>Step 2:</strong>Since 194.75 falls between 169 (13^2) and 225 (15^2), it is between 13 and 15. More precisely, between 13.5 and 14.</p>
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<p><strong>Step 2:</strong>Since 194.75 falls between 169 (13^2) and 225 (15^2), it is between 13 and 15. More precisely, between 13.5 and 14.</p>
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<p><strong>Step 3:</strong>Use the<a>formula</a>: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square). (194.75 - 169) / (225 - 169) ≈ 0.456</p>
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<p><strong>Step 3:</strong>Use the<a>formula</a>: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square). (194.75 - 169) / (225 - 169) ≈ 0.456</p>
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<p><strong>Step 4:</strong>Add this decimal to the lower bound (13) to approximate the square root. 13 + 0.954 ≈ 13.954</p>
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<p><strong>Step 4:</strong>Add this decimal to the lower bound (13) to approximate the square root. 13 + 0.954 ≈ 13.954</p>
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<p>Thus, the approximate square root of 194.75 is 13.954.</p>
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<p>Thus, the approximate square root of 194.75 is 13.954.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 194.75</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 194.75</h2>
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<p>Students do make mistakes while finding the square root, likewise 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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<p>Students do make mistakes while finding the square root, likewise 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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<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 √150?</p>
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<p>Can you help Max find the area of a square box if its side length is given as √150?</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 150 square units.</p>
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<p>The area of the square is 150 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 √150.</p>
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<p>The side length is given as √150.</p>
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<p>Area of the square = side^2 = √150 × √150 = 150.</p>
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<p>Area of the square = side^2 = √150 × √150 = 150.</p>
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<p>Therefore, the area of the square box is 150 square units.</p>
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<p>Therefore, the area of the square box is 150 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 194.75 square feet is built; if each of the sides is √194.75, what will be the square feet of half of the building?</p>
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<p>A square-shaped building measuring 194.75 square feet is built; if each of the sides is √194.75, 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>97.375 square feet</p>
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<p>97.375 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 194.75 by 2 = we get 97.375. So half of the building measures 97.375 square feet.</p>
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<p>Dividing 194.75 by 2 = we get 97.375. So half of the building measures 97.375 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 √194.75 × 5.</p>
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<p>Calculate √194.75 × 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>69.77</p>
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<p>69.77</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 194.75, which is approximately 13.954.</p>
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<p>The first step is to find the square root of 194.75, which is approximately 13.954.</p>
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<p>The second step is to multiply 13.954 by 5. So, 13.954 × 5 ≈ 69.77.</p>
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<p>The second step is to multiply 13.954 by 5. So, 13.954 × 5 ≈ 69.77.</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 (150 + 4.75)?</p>
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<p>What will be the square root of (150 + 4.75)?</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 12.195.</p>
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<p>The square root is approximately 12.195.</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 (150 + 4.75).</p>
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<p>To find the square root, we need to find the sum of (150 + 4.75).</p>
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<p>150 + 4.75 = 154.75, and then √154.75 ≈ 12.195.</p>
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<p>150 + 4.75 = 154.75, and then √154.75 ≈ 12.195.</p>
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<p>Therefore, the square root of (150 + 4.75) is approximately ±12.195.</p>
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<p>Therefore, the square root of (150 + 4.75) is approximately ±12.195.</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 √150 units and the width ‘w’ is 38 units.</p>
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<p>Find the perimeter of the rectangle if its length ‘l’ is √150 units and the width ‘w’ is 38 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 99.48 units.</p>
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<p>We find the perimeter of the rectangle as approximately 99.48 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 × (√150 + 38) ≈ 2 × (12.247 + 38) = 2 × 50.247 ≈ 100.494 units.</p>
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<p>Perimeter = 2 × (√150 + 38) ≈ 2 × (12.247 + 38) = 2 × 50.247 ≈ 100.494 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 194.75</h2>
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<h2>FAQ on Square Root of 194.75</h2>
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<h3>1.What is √194.75 in its simplest form?</h3>
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<h3>1.What is √194.75 in its simplest form?</h3>
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<p>Since 194.75 is not an integer, it cannot be simplified using prime factorization in the traditional sense. It remains √194.75.</p>
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<p>Since 194.75 is not an integer, it cannot be simplified using prime factorization in the traditional sense. It remains √194.75.</p>
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<h3>2.Is 194.75 a perfect square?</h3>
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<h3>2.Is 194.75 a perfect square?</h3>
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<p>No, 194.75 is not a perfect square because its square root is not an integer.</p>
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<p>No, 194.75 is not a perfect square because its square root is not an integer.</p>
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<h3>3.Calculate the square of 194.75.</h3>
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<h3>3.Calculate the square of 194.75.</h3>
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<p>We get the square of 194.75 by multiplying the number by itself, that is 194.75 × 194.75 ≈ 37918.0625.</p>
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<p>We get the square of 194.75 by multiplying the number by itself, that is 194.75 × 194.75 ≈ 37918.0625.</p>
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<h3>4.Is 194.75 a prime number?</h3>
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<h3>4.Is 194.75 a prime number?</h3>
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<p>No, 194.75 is not a<a>prime number</a>because it is not an integer.</p>
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<p>No, 194.75 is not a<a>prime number</a>because it is not an integer.</p>
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<h3>5.What is the approximate decimal value of √194.75?</h3>
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<h3>5.What is the approximate decimal value of √194.75?</h3>
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<p>The approximate decimal value of √194.75 is 13.954.</p>
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<p>The approximate decimal value of √194.75 is 13.954.</p>
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<h2>Important Glossaries for the Square Root of 194.75</h2>
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<h2>Important Glossaries for the Square Root of 194.75</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><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.<strong></strong></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.<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, the positive square root is more commonly used due to its applications in the real world. This is known as the principal square root.</li>
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</ul><ul><li><strong>Principal square root:</strong>A number has both positive and negative square roots; however, the positive square root is more commonly used due to its applications in the real world. This is known as the principal square root.</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><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><ul><li><strong>Perfect square:</strong>A perfect square is a number that can be expressed as the square of an integer, for example: 1, 4, 9, 16, 25, etc.</li>
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</ul><ul><li><strong>Perfect square:</strong>A perfect square is a number that can be expressed as the square of an integer, for example: 1, 4, 9, 16, 25, etc.</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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<p>▶</p>
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<p>▶</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>