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2026-01-01
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2026-02-28
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<p>200 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 fields such as vehicle design and finance. Here, we will discuss the square root of 204.</p>
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<p>If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in fields such as vehicle design and finance. Here, we will discuss the square root of 204.</p>
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<h2>What is the Square Root of 204?</h2>
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<h2>What is the Square Root of 204?</h2>
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<p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 204 is not a<a>perfect square</a>. The square root of 204 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √204, whereas (204)^(1/2) is in exponential form. √204 ≈ 14.28286, 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<a>of</a>the square of the<a>number</a>. 204 is not a<a>perfect square</a>. The square root of 204 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √204, whereas (204)^(1/2) is in exponential form. √204 ≈ 14.28286, 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 204</h2>
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<h2>Finding the Square Root of 204</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 204 by Prime Factorization Method</h2>
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</ul><h2>Square Root of 204 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 204 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 204 is broken down into its prime factors.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 204 Breaking it down, we get 2 x 2 x 3 x 17: 2^2 x 3^1 x 17^1</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 204 Breaking it down, we get 2 x 2 x 3 x 17: 2^2 x 3^1 x 17^1</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 204. The second step is to make pairs of those prime factors. Since 204 is not a perfect square, the digits of the number can’t be grouped in pairs. Therefore, calculating 204 using prime factorization is not straightforward.</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 204. The second step is to make pairs of those prime factors. Since 204 is not a perfect square, the digits of the number can’t be grouped in pairs. Therefore, calculating 204 using prime factorization is not straightforward.</p>
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<h2>Square Root of 204 by Long Division Method</h2>
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<h2>Square Root of 204 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 204, we need to group it as 04 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 204, we need to group it as 04 and 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 2. We can say n is ‘1’ because 1 x 1 is less than or equal to 2. The<a>quotient</a>is 1, and subtracting 1 from 2 gives a<a>remainder</a>of 1.</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 2. We can say n is ‘1’ because 1 x 1 is less than or equal to 2. The<a>quotient</a>is 1, and subtracting 1 from 2 gives a<a>remainder</a>of 1.</p>
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<p><strong>Step 3:</strong>Now let us bring down 04, making the new<a>dividend</a>104. Add the old<a>divisor</a>with the same number 1 + 1 to get 2, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 04, making the new<a>dividend</a>104. Add the old<a>divisor</a>with the same number 1 + 1 to get 2, which will be our new divisor.</p>
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<p><strong>Step 4:</strong>The new divisor will be 2n, where we need to find the value of n.</p>
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<p><strong>Step 4:</strong>The new divisor will be 2n, where we need to find the value of n.</p>
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<p><strong>Step 5:</strong>The next step is finding 2n x n ≤ 104. Let us consider n as 4; now 24 x 4 = 96.</p>
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<p><strong>Step 5:</strong>The next step is finding 2n x n ≤ 104. Let us consider n as 4; now 24 x 4 = 96.</p>
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<p><strong>Step 6:</strong>Subtract 96 from 104, the difference is 8, and the quotient is 14.</p>
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<p><strong>Step 6:</strong>Subtract 96 from 104, the difference is 8, and the quotient is 14.</p>
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<p><strong>Step 7:</strong>Since the remainder 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 800.</p>
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<p><strong>Step 7:</strong>Since the remainder 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 800.</p>
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<p><strong>Step 8:</strong>Find the new divisor, which is 28 because 284 x 4 = 1136.</p>
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<p><strong>Step 8:</strong>Find the new divisor, which is 28 because 284 x 4 = 1136.</p>
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<p><strong>Step 9:</strong>Subtracting 1136 from 8000 gives us 164. Step 10: Now the quotient is 14.2</p>
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<p><strong>Step 9:</strong>Subtracting 1136 from 8000 gives us 164. Step 10: Now the quotient is 14.2</p>
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<p><strong>Step 11:</strong>Continue this process until you reach two decimal places or until the remainder is zero.</p>
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<p><strong>Step 11:</strong>Continue this process until you reach two decimal places or until the remainder is zero.</p>
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<p>So the square root of √204 is approximately 14.28.</p>
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<p>So the square root of √204 is approximately 14.28.</p>
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<h2>Square Root of 204 by Approximation Method</h2>
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<h2>Square Root of 204 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 204 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 204 using the approximation method.</p>
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<p><strong>Step 1:</strong>Find the closest perfect squares to √204. The smallest perfect square less than 204 is 196, and the largest perfect square<a>greater than</a>204 is 225. √204 falls between 14 and 15.</p>
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<p><strong>Step 1:</strong>Find the closest perfect squares to √204. The smallest perfect square less than 204 is 196, and the largest perfect square<a>greater than</a>204 is 225. √204 falls between 14 and 15.</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). Using the formula, (204 - 196) / (225 - 196) ≈ 0.28 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 + 0.28 = 14.28, so the square root of 204 is approximately 14.28.</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). Using the formula, (204 - 196) / (225 - 196) ≈ 0.28 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 + 0.28 = 14.28, so the square root of 204 is approximately 14.28.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 204</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 204</h2>
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<p>Students often make mistakes while finding the square root, such as forgetting about the negative square root, skipping steps in long division, etc. Let us look at a few of these mistakes in detail.</p>
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<p>Students often make mistakes while finding the square root, such as forgetting about the negative square root, skipping steps in long division, etc. Let us look at a few of these mistakes 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 √204?</p>
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<p>Can you help Max find the area of a square box if its side length is given as √204?</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 204 square units.</p>
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<p>The area of the square is approximately 204 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 √204.</p>
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<p>The side length is given as √204.</p>
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<p>Area of the square = side^2 = √204 x √204 = 204.</p>
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<p>Area of the square = side^2 = √204 x √204 = 204.</p>
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<p>Therefore, the area of the square box is approximately 204 square units.</p>
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<p>Therefore, the area of the square box is approximately 204 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 204 square feet is built. If each of the sides is √204, what will be the square feet of half of the building?</p>
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<p>A square-shaped building measuring 204 square feet is built. If each of the sides is √204, 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>102 square feet</p>
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<p>102 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 204 by 2 gives us 102.</p>
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<p>Dividing 204 by 2 gives us 102.</p>
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<p>So half of the building measures 102 square feet.</p>
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<p>So half of the building measures 102 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 √204 x 5.</p>
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<p>Calculate √204 x 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 71.41</p>
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<p>Approximately 71.41</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 204, which is approximately 14.28.</p>
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<p>The first step is to find the square root of 204, which is approximately 14.28.</p>
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<p>The second step is to multiply 14.28 by 5. So, 14.28 x 5 ≈ 71.41.</p>
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<p>The second step is to multiply 14.28 by 5. So, 14.28 x 5 ≈ 71.41.</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 (198 + 6)?</p>
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<p>What will be the square root of (198 + 6)?</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 14.</p>
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<p>The square root is 14.</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 (198 + 6). 198 + 6 = 204, and then √204 ≈ 14.28.</p>
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<p>To find the square root, we need to find the sum of (198 + 6). 198 + 6 = 204, and then √204 ≈ 14.28.</p>
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<p>Therefore, the square root of (198 + 6) is approximately ±14.28.</p>
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<p>Therefore, the square root of (198 + 6) is approximately ±14.28.</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 √204 units and the width ‘w’ is 20 units.</p>
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<p>Find the perimeter of the rectangle if its length ‘l’ is √204 units and the width ‘w’ is 20 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 68.56 units.</p>
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<p>We find the perimeter of the rectangle as approximately 68.56 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 × (√204 + 20) = 2 × (14.28 + 20) = 2 × 34.28 ≈ 68.56 units.</p>
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<p>Perimeter = 2 × (√204 + 20) = 2 × (14.28 + 20) = 2 × 34.28 ≈ 68.56 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 204</h2>
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<h2>FAQ on Square Root of 204</h2>
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<h3>1.What is √204 in its simplest form?</h3>
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<h3>1.What is √204 in its simplest form?</h3>
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<p>The prime factorization of 204 is 2 x 2 x 3 x 17, so the simplest form of √204 = √(2^2 x 3 x 17).</p>
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<p>The prime factorization of 204 is 2 x 2 x 3 x 17, so the simplest form of √204 = √(2^2 x 3 x 17).</p>
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<h3>2.Mention the factors of 204.</h3>
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<h3>2.Mention the factors of 204.</h3>
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<p>Factors of 204 are 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, and 204.</p>
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<p>Factors of 204 are 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, and 204.</p>
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<h3>3.Calculate the square of 204.</h3>
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<h3>3.Calculate the square of 204.</h3>
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<p>We get the square of 204 by multiplying the number by itself, that is 204 x 204 = 41616.</p>
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<p>We get the square of 204 by multiplying the number by itself, that is 204 x 204 = 41616.</p>
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<h3>4.Is 204 a prime number?</h3>
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<h3>4.Is 204 a prime number?</h3>
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<h3>5.204 is divisible by?</h3>
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<h3>5.204 is divisible by?</h3>
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<p>204 has many factors; those are 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, and 204.</p>
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<p>204 has many factors; those are 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, and 204.</p>
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<h2>Important Glossaries for the Square Root of 204</h2>
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<h2>Important Glossaries for the Square Root of 204</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.</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>Principal square root:</strong>A number has both positive and negative square roots. However, it is always the positive square root that has more prominence due to its uses in the real world. That is the reason it is also known as the principal square root.</li>
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</ul><ul><li><strong>Prime factorization:</strong>The expression of a number as a product of its prime factors. For example, the prime factorization of 204 is 2 x 2 x 3 x 17.</li>
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</ul><ul><li><strong>Prime factorization:</strong>The expression of a number as a product of its prime factors. For example, the prime factorization of 204 is 2 x 2 x 3 x 17.</li>
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</ul><ul><li><strong>Long division method:</strong>A step-by-step method used to find the square root of non-perfect squares by dividing and averaging.</li>
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</ul><ul><li><strong>Long division method:</strong>A step-by-step method used to find the square root of non-perfect squares by dividing and averaging.</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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<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>