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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 itself, the result is a square. The inverse of the square is a square root. The square root is used in fields such as vehicle design and finance. Here, we will discuss the square root of 25.25.</p>
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<p>If a number is multiplied by itself, the result is a square. The inverse of the square is a square root. The square root is used in fields such as vehicle design and finance. Here, we will discuss the square root of 25.25.</p>
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<h2>What is the Square Root of 25.25?</h2>
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<h2>What is the Square Root of 25.25?</h2>
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<p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 25.25 is not a<a>perfect square</a>. The square root of 25.25 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √25.25, whereas (25.25)^(1/2) in the exponential form. √25.25 = 5.0249378106, 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>. 25.25 is not a<a>perfect square</a>. The square root of 25.25 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √25.25, whereas (25.25)^(1/2) in the exponential form. √25.25 = 5.0249378106, 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 25.25</h2>
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<h2>Finding the Square Root of 25.25</h2>
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<p>The<a>prime factorization</a>method is used for perfect square numbers. However, for non-perfect square numbers, the long-<a>division</a>method and approximation method are used. Let us now learn the following methods:</p>
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<p>The<a>prime factorization</a>method is used for perfect square numbers. However, for non-perfect square numbers, the long-<a>division</a>method and approximation method are used. Let us now learn the following methods:</p>
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<ul><li>Long division method</li>
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<ul><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 25.25 by Long Division Method</h2>
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</ul><h2>Square Root of 25.25 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>Start by grouping the digits from right to left in pairs. For 25.25, consider 25 and 25 as separate groups.</p>
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<p><strong>Step 1:</strong>Start by grouping the digits from right to left in pairs. For 25.25, consider 25 and 25 as separate groups.</p>
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<p><strong>Step 2:</strong>Find a number whose square is<a>less than</a>or equal to 25. The number is 5, since 5 × 5 = 25. The<a>quotient</a>is 5, and the<a>remainder</a>is 0.</p>
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<p><strong>Step 2:</strong>Find a number whose square is<a>less than</a>or equal to 25. The number is 5, since 5 × 5 = 25. The<a>quotient</a>is 5, and the<a>remainder</a>is 0.</p>
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<p><strong>Step 3:</strong>Bring down the next pair, which is 25, and place it next to the remainder, making it 025. Add the previous<a>divisor</a>, 5, to itself to get 10.</p>
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<p><strong>Step 3:</strong>Bring down the next pair, which is 25, and place it next to the remainder, making it 025. Add the previous<a>divisor</a>, 5, to itself to get 10.</p>
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<p><strong>Step 4:</strong>Find a number (n) such that 10n × n ≤ 25. The number is 2, as 102 × 2 = 204, which is less than 250.</p>
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<p><strong>Step 4:</strong>Find a number (n) such that 10n × n ≤ 25. The number is 2, as 102 × 2 = 204, which is less than 250.</p>
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<p><strong>Step 5:</strong>Subtract 204 from 250, leaving a remainder of 46.</p>
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<p><strong>Step 5:</strong>Subtract 204 from 250, leaving a remainder of 46.</p>
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<p><strong>Step 6:</strong>Bring down another pair of zeros to make the number 4600.</p>
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<p><strong>Step 6:</strong>Bring down another pair of zeros to make the number 4600.</p>
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<p><strong>Step 7:</strong>Continue the process until you reach the desired precision.</p>
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<p><strong>Step 7:</strong>Continue the process until you reach the desired precision.</p>
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<p>The quotient, up to two<a>decimal</a>places, is 5.02.</p>
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<p>The quotient, up to two<a>decimal</a>places, is 5.02.</p>
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<h2>Square Root of 25.25 by Approximation Method</h2>
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<h2>Square Root of 25.25 by Approximation Method</h2>
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<p>The approximation method is another way to find 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 25.25 using the approximation method.</p>
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<p>The approximation method is another way to find 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 25.25 using the approximation method.</p>
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<p><strong>Step 1:</strong>Identify the closest perfect squares to 25.25. The closest perfect squares are 25 (5²) and 36 (6²).</p>
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<p><strong>Step 1:</strong>Identify the closest perfect squares to 25.25. The closest perfect squares are 25 (5²) and 36 (6²).</p>
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<p><strong>Step 2:</strong>Apply the<a>formula</a>:</p>
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<p><strong>Step 2:</strong>Apply the<a>formula</a>:</p>
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<p>(Given number - smaller perfect square) ÷ (larger perfect square - smaller perfect square).</p>
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<p>(Given number - smaller perfect square) ÷ (larger perfect square - smaller perfect square).</p>
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<p><strong>Step 3:</strong>Using the formula, (25.25 - 25) ÷ (36 - 25) = 0.25 ÷ 11 = 0.0227.</p>
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<p><strong>Step 3:</strong>Using the formula, (25.25 - 25) ÷ (36 - 25) = 0.25 ÷ 11 = 0.0227.</p>
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<p><strong>Step 4:</strong>Add this to the square root of the smaller perfect square: 5 + 0.0227 = 5.0227.</p>
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<p><strong>Step 4:</strong>Add this to the square root of the smaller perfect square: 5 + 0.0227 = 5.0227.</p>
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<p>This approximation gives the square root of 25.25 as approximately 5.024.</p>
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<p>This approximation gives the square root of 25.25 as approximately 5.024.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 25.25</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 25.25</h2>
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<p>Students make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division methods. Let us look at a few common mistakes in detail.</p>
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<p>Students make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division methods. 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 √25.25?</p>
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<p>Can you help Max find the area of a square box if its side length is given as √25.25?</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 25.25 square units.</p>
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<p>The area of the square is 25.25 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 a square is given by side².</p>
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<p>The area of a square is given by side².</p>
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<p>The side length is √25.25, so the area is (√25.25)² = 25.25 square units.</p>
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<p>The side length is √25.25, so the area is (√25.25)² = 25.25 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 25.25 square feet is built; if each side is √25.25, what will be the square feet of half of the building?</p>
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<p>A square-shaped building measuring 25.25 square feet is built; if each side is √25.25, 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>12.625 square feet</p>
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<p>12.625 square feet</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Divide the given area by 2 as the building is square-shaped.</p>
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<p>Divide the given area by 2 as the building is square-shaped.</p>
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<p>Dividing 25.25 by 2 gives 12.625 square feet.</p>
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<p>Dividing 25.25 by 2 gives 12.625 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 √25.25 × 5.</p>
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<p>Calculate √25.25 × 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>25.124689053</p>
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<p>25.124689053</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>First, find the square root of 25.25, which is approximately 5.0249378106.</p>
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<p>First, find the square root of 25.25, which is approximately 5.0249378106.</p>
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<p>Then multiply by 5: 5.0249378106 × 5 = 25.124689053.</p>
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<p>Then multiply by 5: 5.0249378106 × 5 = 25.124689053.</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 (20 + 5.25)?</p>
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<p>What will be the square root of (20 + 5.25)?</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 5.0249378106</p>
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<p>The square root is 5.0249378106</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 (20 + 5.25) = 25.25, and then find √25.25 ≈ 5.0249378106.</p>
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<p>To find the square root, sum (20 + 5.25) = 25.25, and then find √25.25 ≈ 5.0249378106.</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 a rectangle if its length ‘l’ is √25.25 units and the width ‘w’ is 8 units.</p>
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<p>Find the perimeter of a rectangle if its length ‘l’ is √25.25 units and the width ‘w’ is 8 units.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The perimeter of the rectangle is 26.0498756212 units.</p>
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<p>The perimeter of the rectangle is 26.0498756212 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 × (√25.25 + 8) = 2 × (5.0249378106 + 8) = 2 × 13.0249378106 = 26.0498756212 units.</p>
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<p>Perimeter = 2 × (√25.25 + 8) = 2 × (5.0249378106 + 8) = 2 × 13.0249378106 = 26.0498756212 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 25.25</h2>
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<h2>FAQ on Square Root of 25.25</h2>
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<h3>1.What is √25.25 in its simplest form?</h3>
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<h3>1.What is √25.25 in its simplest form?</h3>
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<p>√25.25 is already in its simplest form as it cannot be simplified further to an integer or common<a>fraction</a>. It is approximately 5.0249378106.</p>
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<p>√25.25 is already in its simplest form as it cannot be simplified further to an integer or common<a>fraction</a>. It is approximately 5.0249378106.</p>
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<h3>2.Mention the factors of 25.25.</h3>
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<h3>2.Mention the factors of 25.25.</h3>
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<p>Factors of 25.25 as a decimal are not typically listed, but 25.25 is derived from 101/4, so its<a>factors</a>relate to 101 and 4, which are 1, 2, 4, 25.25, 50.5, and 101.</p>
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<p>Factors of 25.25 as a decimal are not typically listed, but 25.25 is derived from 101/4, so its<a>factors</a>relate to 101 and 4, which are 1, 2, 4, 25.25, 50.5, and 101.</p>
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<h3>3.Calculate the square of 25.25.</h3>
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<h3>3.Calculate the square of 25.25.</h3>
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<p>We get the square of 25.25 by multiplying the number by itself: 25.25 × 25.25 = 637.5625.</p>
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<p>We get the square of 25.25 by multiplying the number by itself: 25.25 × 25.25 = 637.5625.</p>
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<h3>4.Is 25.25 a prime number?</h3>
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<h3>4.Is 25.25 a prime number?</h3>
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<p>25.25 is not a<a>prime number</a>as it is not an integer and has decimal points.</p>
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<p>25.25 is not a<a>prime number</a>as it is not an integer and has decimal points.</p>
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<h3>5.25.25 is divisible by?</h3>
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<h3>5.25.25 is divisible by?</h3>
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<p>25.25 is divisible by 1, 5.05, and 25.25.</p>
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<p>25.25 is divisible by 1, 5.05, and 25.25.</p>
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<h2>Important Glossaries for the Square Root of 25.25</h2>
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<h2>Important Glossaries for the Square Root of 25.25</h2>
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<ul><li><strong>Square root:</strong>The square root of a number is a value that, when multiplied by itself, gives the original number. Example: √25.25 ≈ 5.0249. </li>
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<ul><li><strong>Square root:</strong>The square root of a number is a value that, when multiplied by itself, gives the original number. Example: √25.25 ≈ 5.0249. </li>
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<li><strong>Irrational number:</strong>An irrational number cannot be expressed as a simple fraction. It has a non-repeating, non-terminating decimal expansion. </li>
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<li><strong>Irrational number:</strong>An irrational number cannot be expressed as a simple fraction. It has a non-repeating, non-terminating decimal expansion. </li>
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<li><strong>Principal square root:</strong>The principal square root is the positive square root of a number. For example, the principal square root of 25.25 is 5.0249378106. </li>
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<li><strong>Principal square root:</strong>The principal square root is the positive square root of a number. For example, the principal square root of 25.25 is 5.0249378106. </li>
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<li><strong>Decimal:</strong>A decimal is a fraction written in a special form. For example, 0.5 is a decimal and is equal to 1/2. </li>
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<li><strong>Decimal:</strong>A decimal is a fraction written in a special form. For example, 0.5 is a decimal and is equal to 1/2. </li>
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<li><strong>Approximation:</strong>An approximation is a value or quantity that is nearly but not exactly correct. It is used to estimate values when precise figures are not necessary.</li>
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<li><strong>Approximation:</strong>An approximation is a value or quantity that is nearly but not exactly correct. It is used to estimate values when precise figures are not necessary.</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>