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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 fields like vehicle design, finance, etc. Here, we will discuss the square root of 42.25.</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 like vehicle design, finance, etc. Here, we will discuss the square root of 42.25.</p>
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<h2>What is the Square Root of 42.25?</h2>
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<h2>What is the Square Root of 42.25?</h2>
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<p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 42.25 is a<a>perfect square</a>. The square root of 42.25 is expressed in both radical and<a>exponential form</a>.</p>
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<p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 42.25 is a<a>perfect square</a>. The square root of 42.25 is expressed in both radical and<a>exponential form</a>.</p>
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<p>In the radical form, it is expressed as √42.25, whereas (42.25)^(1/2) in exponential form. √42.25 = 6.5, which is a<a>rational number</a>because it can 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>In the radical form, it is expressed as √42.25, whereas (42.25)^(1/2) in exponential form. √42.25 = 6.5, which is a<a>rational number</a>because it can 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 42.25</h2>
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<h2>Finding the Square Root of 42.25</h2>
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<p>The<a>prime factorization</a>method is used for perfect square numbers. For non-perfect square numbers, methods like<a>long division</a>and approximation are used. Since 42.25 is a perfect square, we can directly calculate its<a>square root</a>.</p>
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<p>The<a>prime factorization</a>method is used for perfect square numbers. For non-perfect square numbers, methods like<a>long division</a>and approximation are used. Since 42.25 is a perfect square, we can directly calculate its<a>square root</a>.</p>
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<h3>Square Root of 42.25 by Prime Factorization Method</h3>
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<h3>Square Root of 42.25 by Prime Factorization Method</h3>
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<p>As 42.25 is a perfect square, we can write it as the square of a rational number. Breaking down 42.25, we have:</p>
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<p>As 42.25 is a perfect square, we can write it as the square of a rational number. Breaking down 42.25, we have:</p>
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<p><strong>Step 1:</strong>Write 42.25 as a<a>fraction</a>: 4225/100.</p>
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<p><strong>Step 1:</strong>Write 42.25 as a<a>fraction</a>: 4225/100.</p>
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<p><strong>Step 2:</strong>The square root of 4225 is 65, and the square root of 100 is 10.</p>
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<p><strong>Step 2:</strong>The square root of 4225 is 65, and the square root of 100 is 10.</p>
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<p><strong>Step 3:</strong>Therefore, √42.25 = 65/10 = 6.5. Since 42.25 is already a perfect square, the calculation confirms that the square root is 6.5.</p>
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<p><strong>Step 3:</strong>Therefore, √42.25 = 65/10 = 6.5. Since 42.25 is already a perfect square, the calculation confirms that the square root is 6.5.</p>
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<h2>Square Root of 42.25 by Long Division Method</h2>
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<h2>Square Root of 42.25 by Long Division Method</h2>
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<p>For perfect square numbers like 42.25, the long<a>division</a>method can verify the square root:</p>
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<p>For perfect square numbers like 42.25, the long<a>division</a>method can verify the square root:</p>
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<p><strong>Step 1:</strong>Start with 42.25 and group the numbers from the<a>decimal</a>point into pairs: 42 | 25.</p>
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<p><strong>Step 1:</strong>Start with 42.25 and group the numbers from the<a>decimal</a>point into pairs: 42 | 25.</p>
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<p><strong>Step 2:</strong>Find a number whose square is closest to 42. This number is 6 because 6 × 6 = 36.</p>
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<p><strong>Step 2:</strong>Find a number whose square is closest to 42. This number is 6 because 6 × 6 = 36.</p>
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<p><strong>Step 3:</strong>Subtract 36 from 42,<a>remainder</a>is 6. Bring down 25 to make it 625.</p>
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<p><strong>Step 3:</strong>Subtract 36 from 42,<a>remainder</a>is 6. Bring down 25 to make it 625.</p>
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<p><strong>Step 4:</strong>Double the<a>divisor</a>, 6, to get 12. Now, find a digit, n, such that 12n × n is close to 625. n is 5, since 125 × 5 = 625.</p>
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<p><strong>Step 4:</strong>Double the<a>divisor</a>, 6, to get 12. Now, find a digit, n, such that 12n × n is close to 625. n is 5, since 125 × 5 = 625.</p>
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<p><strong>Step 5:</strong>Subtract 625 from 625 to get 0, confirming the square root is 6.5.</p>
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<p><strong>Step 5:</strong>Subtract 625 from 625 to get 0, confirming the square root is 6.5.</p>
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<h2>Square Root of 42.25 by Approximation Method</h2>
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<h2>Square Root of 42.25 by Approximation Method</h2>
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<p>The approximation method can also be used to find the square roots:</p>
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<p>The approximation method can also be used to find the square roots:</p>
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<p><strong>Step 1:</strong>Identify the perfect squares around 42.25, which are 36 (6^2) and 49 (7^2).</p>
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<p><strong>Step 1:</strong>Identify the perfect squares around 42.25, which are 36 (6^2) and 49 (7^2).</p>
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<p><strong>Step 2:</strong>Since 42.25 is exactly halfway between 36 and 49, √42.25 is halfway between 6 and 7.</p>
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<p><strong>Step 2:</strong>Since 42.25 is exactly halfway between 36 and 49, √42.25 is halfway between 6 and 7.</p>
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<p><strong>Step 3:</strong>Calculate the<a>average</a>: (6 + 7) / 2 = 6.5. Thus, the square root of 42.25 is precisely 6.5.</p>
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<p><strong>Step 3:</strong>Calculate the<a>average</a>: (6 + 7) / 2 = 6.5. Thus, the square root of 42.25 is precisely 6.5.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 42.25</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 42.25</h2>
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<p>Students can make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps. Let us look at a few common mistakes in detail.</p>
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<p>Students can make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps. Let us look at a few common mistakes 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 √42.25?</p>
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<p>Can you help Max find the area of a square box if its side length is given as √42.25?</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 42.25 square units.</p>
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<p>The area of the square is 42.25 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. The side length is given as √42.25.</p>
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<p>The area of the square = side^2. The side length is given as √42.25.</p>
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<p>Area of the square = side^2 = (√42.25) × (√42.25) = 6.5 × 6.5 = 42.25.</p>
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<p>Area of the square = side^2 = (√42.25) × (√42.25) = 6.5 × 6.5 = 42.25.</p>
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<p>Therefore, the area of the square box is 42.25 square units.</p>
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<p>Therefore, the area of the square box is 42.25 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 garden measuring 42.25 square meters is built; if each of the sides is √42.25, what will be the square meters of half of the garden?</p>
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<p>A square-shaped garden measuring 42.25 square meters is built; if each of the sides is √42.25, what will be the square meters of half of the garden?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>21.125 square meters</p>
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<p>21.125 square meters</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Divide the area by 2 as the garden is square-shaped.</p>
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<p>Divide the area by 2 as the garden is square-shaped.</p>
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<p>Dividing 42.25 by 2 = 21.125.</p>
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<p>Dividing 42.25 by 2 = 21.125.</p>
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<p>So half of the garden measures 21.125 square meters.</p>
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<p>So half of the garden measures 21.125 square meters.</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 √42.25 × 4.</p>
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<p>Calculate √42.25 × 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>26</p>
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<p>26</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 42.25, which is 6.5.</p>
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<p>The first step is to find the square root of 42.25, which is 6.5.</p>
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<p>The second step is to multiply 6.5 by 4. So 6.5 × 4 = 26.</p>
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<p>The second step is to multiply 6.5 by 4. So 6.5 × 4 = 26.</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 (36 + 6.25)?</p>
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<p>What will be the square root of (36 + 6.25)?</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 6.5</p>
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<p>The square root is 6.5</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, sum (36 + 6.25). 36 + 6.25 = 42.25, and then √42.25 = 6.5.</p>
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<p>To find the square root, sum (36 + 6.25). 36 + 6.25 = 42.25, and then √42.25 = 6.5.</p>
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<p>Therefore, the square root of (36 + 6.25) is ±6.5.</p>
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<p>Therefore, the square root of (36 + 6.25) is ±6.5.</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 √42.25 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 √42.25 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 53 units.</p>
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<p>We find the perimeter of the rectangle as 53 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 × (√42.25 + 20) = 2 × (6.5 + 20) = 2 × 26.5 = 53 units.</p>
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<p>Perimeter = 2 × (√42.25 + 20) = 2 × (6.5 + 20) = 2 × 26.5 = 53 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 42.25</h2>
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<h2>FAQ on Square Root of 42.25</h2>
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<h3>1.What is √42.25 in its simplest form?</h3>
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<h3>1.What is √42.25 in its simplest form?</h3>
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<p>The simplest form of √42.25 is 6.5, as it is a perfect square.</p>
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<p>The simplest form of √42.25 is 6.5, as it is a perfect square.</p>
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<h3>2.Mention the factors of 42.25.</h3>
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<h3>2.Mention the factors of 42.25.</h3>
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<p>The<a>factors</a>of 42.25 as a decimal are derived from its square root: 1, 6.5, and 42.25.</p>
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<p>The<a>factors</a>of 42.25 as a decimal are derived from its square root: 1, 6.5, and 42.25.</p>
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<h3>3.Calculate the square of 42.25.</h3>
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<h3>3.Calculate the square of 42.25.</h3>
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<p>The square of 42.25 is calculated by multiplying the number by itself: 42.25 × 42.25 = 1785.0625.</p>
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<p>The square of 42.25 is calculated by multiplying the number by itself: 42.25 × 42.25 = 1785.0625.</p>
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<h3>4.Is 42.25 a prime number?</h3>
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<h3>4.Is 42.25 a prime number?</h3>
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<p>42.25 is not a<a>prime number</a>, as it has more than two factors.</p>
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<p>42.25 is not a<a>prime number</a>, as it has more than two factors.</p>
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<h3>5.42.25 is divisible by?</h3>
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<h3>5.42.25 is divisible by?</h3>
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<p>42.25 is divisible by 1, 6.5, and 42.25.</p>
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<p>42.25 is divisible by 1, 6.5, and 42.25.</p>
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<h2>Important Glossaries for the Square Root of 42.25</h2>
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<h2>Important Glossaries for the Square Root of 42.25</h2>
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<ul><li><strong>Square root:</strong>A square root is the inverse of squaring a number. For example, 6.5^2 = 42.25, and the square root is √42.25 = 6.5. </li>
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<ul><li><strong>Square root:</strong>A square root is the inverse of squaring a number. For example, 6.5^2 = 42.25, and the square root is √42.25 = 6.5. </li>
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<li><strong>Rational number:</strong>A rational number can be expressed in the form of p/q, where q is not zero, and p and q are integers. </li>
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<li><strong>Rational number:</strong>A rational number can be expressed in the form of p/q, where q is not zero, and p and q are integers. </li>
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<li><strong>Perfect square:</strong>A perfect square is a number that is the square of an integer or rational number. Example: 42.25 is a perfect square because it is 6.5^2. </li>
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<li><strong>Perfect square:</strong>A perfect square is a number that is the square of an integer or rational number. Example: 42.25 is a perfect square because it is 6.5^2. </li>
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<li><strong>Decimal:</strong>A decimal is a number that contains a whole number and a fractional part separated by a decimal point, such as 6.5. </li>
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<li><strong>Decimal:</strong>A decimal is a number that contains a whole number and a fractional part separated by a decimal point, such as 6.5. </li>
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<li><strong>Long division method:</strong>A technique used to find the square root of a number, especially for non-perfect squares, involving dividing the number into pairs from the decimal point.</li>
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<li><strong>Long division method:</strong>A technique used to find the square root of a number, especially for non-perfect squares, involving dividing the number into pairs from the decimal point.</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>