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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 12.25.</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 12.25.</p>
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<h2>What is the Square Root of 12.25?</h2>
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<h2>What is the Square Root of 12.25?</h2>
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<p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 12.25 is a<a>perfect square</a>. The square root of 12.25 is expressed in both radical and<a>exponential form</a>. In radical form, it is expressed as √12.25, whereas (12.25)^(1/2) in exponential form. √12.25 = 3.5, 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>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 12.25 is a<a>perfect square</a>. The square root of 12.25 is expressed in both radical and<a>exponential form</a>. In radical form, it is expressed as √12.25, whereas (12.25)^(1/2) in exponential form. √12.25 = 3.5, 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 12.25</h2>
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<h2>Finding the Square Root of 12.25</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 the<a>long 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. For non-perfect square numbers, methods like the<a>long 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 12.25 by Prime Factorization Method</h2>
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</ul><h2>Square Root of 12.25 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 12.25 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 12.25 is broken down into its prime factors.</p>
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<p><strong>Step 1:</strong>Recognize 12.25 as 1225/100.</p>
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<p><strong>Step 1:</strong>Recognize 12.25 as 1225/100.</p>
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<p><strong>Step 2:</strong>Find the prime factors of 1225 and 100. 1225 = 5 x 5 x 7 x 7, and 100 = 2 x 2 x 5 x 5.</p>
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<p><strong>Step 2:</strong>Find the prime factors of 1225 and 100. 1225 = 5 x 5 x 7 x 7, and 100 = 2 x 2 x 5 x 5.</p>
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<p><strong>Step 3:</strong>Taking the<a>square root</a>, √12.25 = √(1225/100) = (5 x 7) / (2 x 5) = 7/2 = 3.5.</p>
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<p><strong>Step 3:</strong>Taking the<a>square root</a>, √12.25 = √(1225/100) = (5 x 7) / (2 x 5) = 7/2 = 3.5.</p>
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<h2>Square Root of 12.25 by Long Division Method</h2>
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<h2>Square Root of 12.25 by Long Division Method</h2>
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<p>The long<a>division</a>method is particularly useful for non-perfect square numbers, but it can also be used to understand perfect squares. Let us now learn how to find the square root using the long division method, step by step.</p>
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<p>The long<a>division</a>method is particularly useful for non-perfect square numbers, but it can also be used to understand perfect squares. Let us now learn how to find the square root using the long division method, step by step.</p>
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<p><strong>Step 1:</strong>Group the numbers from right to left. For 12.25, consider 1225.</p>
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<p><strong>Step 1:</strong>Group the numbers from right to left. For 12.25, consider 1225.</p>
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<p><strong>Step 2:</strong>Find n whose square is closest to 12. We can say n is 3 because 3 x 3 = 9, which is<a>less than</a>12.</p>
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<p><strong>Step 2:</strong>Find n whose square is closest to 12. We can say n is 3 because 3 x 3 = 9, which is<a>less than</a>12.</p>
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<p><strong>Step 3:</strong>Bring down the next pair (25) to make it 325. Double the current<a>quotient</a>(3), making it 6, and use it to find the next digit.</p>
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<p><strong>Step 3:</strong>Bring down the next pair (25) to make it 325. Double the current<a>quotient</a>(3), making it 6, and use it to find the next digit.</p>
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<p><strong>Step 4:</strong>Estimate the next digit (5) such that 65 x 5 = 325.</p>
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<p><strong>Step 4:</strong>Estimate the next digit (5) such that 65 x 5 = 325.</p>
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<p><strong>Step 5:</strong>The quotient is 3.5, which is the square root of 12.25.</p>
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<p><strong>Step 5:</strong>The quotient is 3.5, which is the square root of 12.25.</p>
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<h2>Square Root of 12.25 by Approximation Method</h2>
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<h2>Square Root of 12.25 by Approximation Method</h2>
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<p>The approximation method is another method for finding square roots and is an easy method to find the square root of a given number. Now let us learn how to find the square root of 12.25 using the approximation method.</p>
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<p>The approximation method is another method for finding square roots and is an easy method to find the square root of a given number. Now let us learn how to find the square root of 12.25 using the approximation method.</p>
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<p><strong>Step 1:</strong>Find two perfect squares between which 12.25 lies. It is between 9 and 16.</p>
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<p><strong>Step 1:</strong>Find two perfect squares between which 12.25 lies. It is between 9 and 16.</p>
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<p><strong>Step 2:</strong>Since 12.25 is closer to 16, approximate starting from √16 = 4. Decrease gradually to find the precise value.</p>
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<p><strong>Step 2:</strong>Since 12.25 is closer to 16, approximate starting from √16 = 4. Decrease gradually to find the precise value.</p>
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<p><strong>Step 3:</strong>Using the approximation, √12.25 is exactly 3.5.</p>
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<p><strong>Step 3:</strong>Using the approximation, √12.25 is exactly 3.5.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 12.25</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 12.25</h2>
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<p>Students do make mistakes while finding the square root, such as 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, such as 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 √12.25?</p>
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<p>Can you help Max find the area of a square box if its side length is given as √12.25?</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 12.25 square units.</p>
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<p>The area of the square is 12.25 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 = side².</p>
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<p>The area of the square = side².</p>
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<p>The side length is given as √12.25.</p>
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<p>The side length is given as √12.25.</p>
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<p>Area of the square = side² = √12.25 x √12.25 = 3.5 × 3.5 = 12.25.</p>
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<p>Area of the square = side² = √12.25 x √12.25 = 3.5 × 3.5 = 12.25.</p>
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<p>Therefore, the area of the square box is 12.25 square units.</p>
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<p>Therefore, the area of the square box is 12.25 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 building measuring 12.25 square feet is built; if each of the sides is √12.25, what will be the square feet of half of the building?</p>
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<p>A square-shaped building measuring 12.25 square feet is built; if each of the sides is √12.25, 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>6.125 square feet.</p>
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<p>6.125 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 12.25 by 2, we get 6.125.</p>
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<p>Dividing 12.25 by 2, we get 6.125.</p>
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<p>So half of the building measures 6.125 square feet.</p>
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<p>So half of the building measures 6.125 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 √12.25 x 5.</p>
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<p>Calculate √12.25 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>17.5</p>
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<p>17.5</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 12.25, which is 3.5.</p>
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<p>The first step is to find the square root of 12.25, which is 3.5.</p>
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<p>The second step is to multiply 3.5 with 5. So 3.5 x 5 = 17.5.</p>
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<p>The second step is to multiply 3.5 with 5. So 3.5 x 5 = 17.5.</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 (9 + 3.25)?</p>
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<p>What will be the square root of (9 + 3.25)?</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 3.5.</p>
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<p>The square root is 3.5.</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, we need to find the sum of (9 + 3.25). 9 + 3.25 = 12.25, and then √12.25 = 3.5.</p>
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<p>To find the square root, we need to find the sum of (9 + 3.25). 9 + 3.25 = 12.25, and then √12.25 = 3.5.</p>
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<p>Therefore, the square root of (9 + 3.25) is ±3.5.</p>
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<p>Therefore, the square root of (9 + 3.25) is ±3.5.</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 √12.25 units and the width ‘w’ is 5 units.</p>
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<p>Find the perimeter of the rectangle if its length ‘l’ is √12.25 units and the width ‘w’ is 5 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 17 units.</p>
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<p>We find the perimeter of the rectangle as 17 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 × (√12.25 + 5) = 2 × (3.5 + 5) = 2 × 8.5 = 17 units.</p>
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<p>Perimeter = 2 × (√12.25 + 5) = 2 × (3.5 + 5) = 2 × 8.5 = 17 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 12.25</h2>
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<h2>FAQ on Square Root of 12.25</h2>
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<h3>1.What is √12.25 in its simplest form?</h3>
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<h3>1.What is √12.25 in its simplest form?</h3>
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<p>The prime factorization of 12.25 is 5 x 5 x 7 x 7, so the simplest form of √12.25 = 3.5.</p>
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<p>The prime factorization of 12.25 is 5 x 5 x 7 x 7, so the simplest form of √12.25 = 3.5.</p>
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<h3>2.Mention the factors of 12.25.</h3>
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<h3>2.Mention the factors of 12.25.</h3>
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<p>Factors of 12.25 when expressed as a<a>fraction</a>are 1, 2.5, 3.5, 5, 7, and 12.25.</p>
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<p>Factors of 12.25 when expressed as a<a>fraction</a>are 1, 2.5, 3.5, 5, 7, and 12.25.</p>
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<h3>3.Calculate the square of 12.25.</h3>
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<h3>3.Calculate the square of 12.25.</h3>
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<p>We get the square of 12.25 by multiplying the number by itself, that is 12.25 x 12.25 = 150.0625.</p>
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<p>We get the square of 12.25 by multiplying the number by itself, that is 12.25 x 12.25 = 150.0625.</p>
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<h3>4.Is 12.25 a prime number?</h3>
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<h3>4.Is 12.25 a prime number?</h3>
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<p>12.25 is not a<a>prime number</a>. It is a perfect square of a rational number.</p>
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<p>12.25 is not a<a>prime number</a>. It is a perfect square of a rational number.</p>
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<h3>5.12.25 is divisible by?</h3>
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<h3>5.12.25 is divisible by?</h3>
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<p>12.25 is divisible by 1, 2.5, 3.5, 5, and 7.</p>
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<p>12.25 is divisible by 1, 2.5, 3.5, 5, and 7.</p>
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<h2>Important Glossaries for the Square Root of 12.25</h2>
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<h2>Important Glossaries for the Square Root of 12.25</h2>
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<ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: 3.5² = 12.25, and the inverse of the square is the square root, that is √12.25 = 3.5. </li>
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<ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: 3.5² = 12.25, and the inverse of the square is the square root, that is √12.25 = 3.5. </li>
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<li><strong>Rational number:</strong>A rational number is a number that can be written in the form of p/q, q is not equal to zero, and p and q are integers. </li>
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<li><strong>Rational number:</strong>A rational number is a number that can be written in the form of p/q, q is not equal to zero, and p and q are integers. </li>
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<li><strong>Perfect square:</strong>A number that is the square of an integer or a rational number. Example: 12.25 is a perfect square because it is 3.5². </li>
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<li><strong>Perfect square:</strong>A number that is the square of an integer or a rational number. Example: 12.25 is a perfect square because it is 3.5². </li>
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<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, 3.5, 7.86, and 9.42 are decimals. </li>
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<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, 3.5, 7.86, and 9.42 are decimals. </li>
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<li><strong>Quotient:</strong>The result obtained by dividing one quantity by another. For example, in 12.25 ÷ 3.5 = 3.5, the quotient is 3.5.</li>
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<li><strong>Quotient:</strong>The result obtained by dividing one quantity by another. For example, in 12.25 ÷ 3.5 = 3.5, the quotient is 3.5.</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>