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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 such as vehicle design, finance, etc. Here, we will discuss the square root of 90.25.</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 such as vehicle design, finance, etc. Here, we will discuss the square root of 90.25.</p>
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<h2>What is the Square Root of 90.25?</h2>
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<h2>What is the Square Root of 90.25?</h2>
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<p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 90.25 is a<a>perfect square</a>. The square root of 90.25 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>. 90.25 is a<a>perfect square</a>. The square root of 90.25 is expressed in both radical and<a>exponential form</a>.</p>
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<p>In the radical form, it is expressed as √90.25, whereas in the exponential form it is (90.25)(1/2). The square root of 90.25 is 9.5, 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 √90.25, whereas in the exponential form it is (90.25)(1/2). The square root of 90.25 is 9.5, 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 90.25</h2>
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<h2>Finding the Square Root of 90.25</h2>
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<p>The<a>prime factorization</a>method is used for perfect square numbers. For non-perfect squares, methods such as the long-<a>division</a>method and approximation method are used. However, since 90.25 is a perfect square, we can directly find its<a>square root</a>. 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 squares, methods such as the long-<a>division</a>method and approximation method are used. However, since 90.25 is a perfect square, we can directly find its<a>square root</a>. Let us now learn the following methods: -</p>
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<ol><li>Prime factorization method </li>
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<ol><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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</ol><h2>Square Root of 90.25 by Prime Factorization Method</h2>
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</ol><h2>Square Root of 90.25 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. 90.25 is a perfect square and can be expressed as (9.5)2.</p>
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<p>The<a>product</a>of prime<a>factors</a>is the prime factorization of a number. 90.25 is a perfect square and can be expressed as (9.5)2.</p>
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<p>Thus, the prime factorization method confirms that 90.25 is a perfect square, and its square root is 9.5.</p>
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<p>Thus, the prime factorization method confirms that 90.25 is a perfect square, and its square root is 9.5.</p>
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<h2>Square Root of 90.25 by Long Division Method</h2>
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<h2>Square Root of 90.25 by Long Division Method</h2>
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<p>The<a>long division</a>method can also be used for finding the square root of perfect squares. For 90.25, we can follow these steps:</p>
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<p>The<a>long division</a>method can also be used for finding the square root of perfect squares. For 90.25, we can follow these steps:</p>
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<p><strong>Step 1:</strong>Group the numbers from right to left. For 90.25, we consider it as 90.25.</p>
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<p><strong>Step 1:</strong>Group the numbers from right to left. For 90.25, we consider it as 90.25.</p>
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<p><strong>Step 2:</strong>Find a number whose square is closest to 90 without exceeding it. Here, that number is 9, because 9 × 9 = 81.</p>
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<p><strong>Step 2:</strong>Find a number whose square is closest to 90 without exceeding it. Here, that number is 9, because 9 × 9 = 81.</p>
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<p><strong>Step 3:</strong>Subtract 81 from 90, which gives 9. Bring down 25 to make it 925.</p>
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<p><strong>Step 3:</strong>Subtract 81 from 90, which gives 9. Bring down 25 to make it 925.</p>
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<p><strong>Step 4:</strong>Double the<a>divisor</a>(9) to get 18. Next, find a number n such that 18n × n is closest to 925 without exceeding it. Here, n is 5, because 185 × 5 = 925.</p>
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<p><strong>Step 4:</strong>Double the<a>divisor</a>(9) to get 18. Next, find a number n such that 18n × n is closest to 925 without exceeding it. Here, n is 5, because 185 × 5 = 925.</p>
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<p><strong>Step 5:</strong>Subtract 925 from 925, giving a<a>remainder</a>of 0. The<a>quotient</a>is 9.5.</p>
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<p><strong>Step 5:</strong>Subtract 925 from 925, giving a<a>remainder</a>of 0. The<a>quotient</a>is 9.5.</p>
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<p>So the square root of √90.25 is 9.5.</p>
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<p>So the square root of √90.25 is 9.5.</p>
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<h2>Square Root of 90.25 by Approximation Method</h2>
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<h2>Square Root of 90.25 by Approximation Method</h2>
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<p>The approximation method is also an easy way to find the square root of a given number. Here, however, since 90.25 is a perfect square, we can directly approximate it as follows:</p>
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<p>The approximation method is also an easy way to find the square root of a given number. Here, however, since 90.25 is a perfect square, we can directly approximate it as follows:</p>
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<p><strong>Step 1:</strong>Identify the number nearest to 90.25 that is a perfect square. Both 81 (92) and 100 (102) are near, but 90.25 is exactly 9.52.</p>
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<p><strong>Step 1:</strong>Identify the number nearest to 90.25 that is a perfect square. Both 81 (92) and 100 (102) are near, but 90.25 is exactly 9.52.</p>
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<p>Therefore, the square root of 90.25 is 9.5.</p>
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<p>Therefore, the square root of 90.25 is 9.5.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 90.25</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 90.25</h2>
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<p>Students often make mistakes while finding the square root, such as forgetting about the negative square root or incorrectly applying methods. Let's look at a few common 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 or incorrectly applying methods. Let's 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 √90.25?</p>
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<p>Can you help Max find the area of a square box if its side length is given as √90.25?</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 90.25 square units.</p>
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<p>The area of the square is 90.25 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 √90.25.</p>
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<p>The side length is given as √90.25.</p>
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<p>Area of the square = side2 = √90.25 × √90.25 = 9.5 × 9.5 = 90.25.</p>
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<p>Area of the square = side2 = √90.25 × √90.25 = 9.5 × 9.5 = 90.25.</p>
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<p>Therefore, the area of the square box is 90.25 square units.</p>
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<p>Therefore, the area of the square box is 90.25 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 90.25 square feet is built; if each of the sides is √90.25, what will be the square feet of half of the building?</p>
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<p>A square-shaped building measuring 90.25 square feet is built; if each of the sides is √90.25, 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>45.125 square feet</p>
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<p>45.125 square feet</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>We can divide the given area by 2 as the building is square-shaped. Dividing 90.25 by 2 gives us 45.125.</p>
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<p>We can divide the given area by 2 as the building is square-shaped. Dividing 90.25 by 2 gives us 45.125.</p>
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<p>So half of the building measures 45.125 square feet.</p>
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<p>So half of the building measures 45.125 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 √90.25 × 5.</p>
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<p>Calculate √90.25 × 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>47.5</p>
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<p>47.5</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 90.25, which is 9.5.</p>
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<p>The first step is to find the square root of 90.25, which is 9.5.</p>
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<p>The second step is to multiply 9.5 by 5.</p>
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<p>The second step is to multiply 9.5 by 5.</p>
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<p>So 9.5 × 5 = 47.5.</p>
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<p>So 9.5 × 5 = 47.5.</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 (81 + 9.25)?</p>
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<p>What will be the square root of (81 + 9.25)?</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 9.5.</p>
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<p>The square root is 9.5.</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 calculate the sum of 81 + 9.25. 81 + 9.25 = 90.25, and then √90.25 = 9.5.</p>
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<p>To find the square root, we calculate the sum of 81 + 9.25. 81 + 9.25 = 90.25, and then √90.25 = 9.5.</p>
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<p>Therefore, the square root of (81 + 9.25) is ±9.5.</p>
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<p>Therefore, the square root of (81 + 9.25) is ±9.5.</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 √90.25 units and the width ‘w’ is 10 units.</p>
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<p>Find the perimeter of the rectangle if its length ‘l’ is √90.25 units and the width ‘w’ is 10 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 39 units.</p>
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<p>We find the perimeter of the rectangle as 39 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 × (√90.25 + 10)</p>
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<p>Perimeter = 2 × (√90.25 + 10)</p>
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<p>= 2 × (9.5 + 10)</p>
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<p>= 2 × (9.5 + 10)</p>
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<p>= 2 × 19.5 = 39 units.</p>
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<p>= 2 × 19.5 = 39 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 90.25</h2>
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<h2>FAQ on Square Root of 90.25</h2>
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<h3>1.What is √90.25 in its simplest form?</h3>
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<h3>1.What is √90.25 in its simplest form?</h3>
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<p>√90.25 is already in its simplest form as 9.5 since 90.25 is a perfect square, represented as (9.5)^2.</p>
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<p>√90.25 is already in its simplest form as 9.5 since 90.25 is a perfect square, represented as (9.5)^2.</p>
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<h3>2.Mention the factors of 90.25.</h3>
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<h3>2.Mention the factors of 90.25.</h3>
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<p>Factors of 90.25 are 1, 9.5, and 90.25, considering it as the square of 9.5.</p>
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<p>Factors of 90.25 are 1, 9.5, and 90.25, considering it as the square of 9.5.</p>
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<h3>3.Calculate the square of 9.5.</h3>
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<h3>3.Calculate the square of 9.5.</h3>
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<p>We get the square of 9.5 by multiplying the number by itself, that is 9.5 × 9.5 = 90.25.</p>
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<p>We get the square of 9.5 by multiplying the number by itself, that is 9.5 × 9.5 = 90.25.</p>
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<h3>4.Is 90.25 a prime number?</h3>
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<h3>4.Is 90.25 a prime number?</h3>
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<h3>5.90.25 is divisible by?</h3>
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<h3>5.90.25 is divisible by?</h3>
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<p>90.25 is divisible by 1, 9.5, and 90.25.</p>
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<p>90.25 is divisible by 1, 9.5, and 90.25.</p>
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<h2>Important Glossaries for the Square Root of 90.25</h2>
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<h2>Important Glossaries for the Square Root of 90.25</h2>
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<ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: 9.5^2 = 90.25 and the inverse of the square is the square root, that is √90.25 = 9.5.</li>
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<ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: 9.5^2 = 90.25 and the inverse of the square is the square root, that is √90.25 = 9.5.</li>
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</ul><ul><li><strong>Rational number:</strong>A rational number can be written in the form of p/q, where p and q are integers and q ≠ 0.</li>
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</ul><ul><li><strong>Rational number:</strong>A rational number can be written in the form of p/q, where p and q are integers and q ≠ 0.</li>
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</ul><ul><li><strong>Perfect square:</strong>A number that is the square of an integer is a perfect square. Example: 90.25 is a perfect square because it is 9.52 </li>
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</ul><ul><li><strong>Perfect square:</strong>A number that is the square of an integer is a perfect square. Example: 90.25 is a perfect square because it is 9.52 </li>
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</ul><ul><li><strong>Decimal:</strong>If a number has a whole number and a fraction in a single number, it is called a decimal. Example: 9.5 is a decimal.</li>
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</ul><ul><li><strong>Decimal:</strong>If a number has a whole number and a fraction in a single number, it is called a decimal. Example: 9.5 is a decimal.</li>
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</ul><ul><li><strong>Principal square root:</strong>A number has both positive and negative square roots; however, the positive square root is often used in real-world applications and is known as the principal square root.</li>
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</ul><ul><li><strong>Principal square root:</strong>A number has both positive and negative square roots; however, the positive square root is often used in real-world applications and is known as the principal square root.</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>