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2026-01-01
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2026-02-28
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<p>179 Learners</p>
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<p>Last updated on<strong>August 5, 2025</strong></p>
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<p>Last updated on<strong>August 5, 2025</strong></p>
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<p>If a number is multiplied by itself, the result is a square. The inverse of the square is a square root. The square root is used in various fields such as vehicle design, finance, etc. Here, we will discuss the square root of 8825.</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 various fields such as vehicle design, finance, etc. Here, we will discuss the square root of 8825.</p>
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<h2>What is the Square Root of 8825?</h2>
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<h2>What is the Square Root of 8825?</h2>
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<p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 8825 is not a<a>perfect square</a>. The square root of 8825 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √8825, whereas in the exponential form it is expressed as 8825^(1/2). √8825 ≈ 93.9685, which is an<a>irrational number</a>because it cannot be expressed in the form of p/q, where p and q are<a>integers</a>and q ≠ 0.</p>
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<p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 8825 is not a<a>perfect square</a>. The square root of 8825 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √8825, whereas in the exponential form it is expressed as 8825^(1/2). √8825 ≈ 93.9685, 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 8825</h2>
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<h2>Finding the Square Root of 8825</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<a>long division</a>method and approximation method are used. Let us now learn about 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<a>long division</a>method and approximation method are used. Let us now learn about 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 8825 by Prime Factorization Method</h2>
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</ul><h2>Square Root of 8825 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 8825 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 8825 is broken down into its prime factors.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 8825</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 8825</p>
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<p>Breaking it down, we get 5 x 5 x 7 x 13 x 19: 5^2 x 7 x 13 x 19</p>
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<p>Breaking it down, we get 5 x 5 x 7 x 13 x 19: 5^2 x 7 x 13 x 19</p>
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<p><strong>Step 2:</strong>Now we have found the prime factors of 8825. The second step is to make pairs of those prime factors. Since 8825 is not a perfect square, the digits of the number can’t be completely grouped in pairs. Therefore, calculating √8825 using prime factorization is not straightforward.</p>
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<p><strong>Step 2:</strong>Now we have found the prime factors of 8825. The second step is to make pairs of those prime factors. Since 8825 is not a perfect square, the digits of the number can’t be completely grouped in pairs. Therefore, calculating √8825 using prime factorization is not straightforward.</p>
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<h2>Square Root of 8825 by Long Division Method</h2>
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<h2>Square Root of 8825 by Long Division Method</h2>
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<p>The long<a>division</a>method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the<a>square root</a>using the long division method, step by step.</p>
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<p>The long<a>division</a>method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the<a>square root</a>using the long division method, step by step.</p>
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<p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 8825, we need to group it as 88 and 25.</p>
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<p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 8825, we need to group it as 88 and 25.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is<a>less than</a>or equal to 88. We can say n is ‘9’ because 9 x 9 = 81 which is less than 88. Now the<a>quotient</a>is 9, after subtracting 81 from 88, the<a>remainder</a>is 7.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is<a>less than</a>or equal to 88. We can say n is ‘9’ because 9 x 9 = 81 which is less than 88. Now the<a>quotient</a>is 9, after subtracting 81 from 88, the<a>remainder</a>is 7.</p>
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<p><strong>Step 3:</strong>Now let us bring down 25, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number (9 + 9) to get 18, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 25, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number (9 + 9) to get 18, which will be our new divisor.</p>
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<p><strong>Step 4:</strong>The new divisor will be 18_, and we need to find the value of n.</p>
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<p><strong>Step 4:</strong>The new divisor will be 18_, and we need to find the value of n.</p>
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<p><strong>Step 5:</strong>The next step is finding 18n x n ≤ 725. Let us consider n as 4. Now, 184 x 4 = 736, which exceeds 725. Try n as 3. Now 183 x 3 = 549 which is less than 725.</p>
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<p><strong>Step 5:</strong>The next step is finding 18n x n ≤ 725. Let us consider n as 4. Now, 184 x 4 = 736, which exceeds 725. Try n as 3. Now 183 x 3 = 549 which is less than 725.</p>
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<p><strong>Step 6:</strong>Subtract 549 from 725, the difference is 176, and the quotient is 93.</p>
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<p><strong>Step 6:</strong>Subtract 549 from 725, the difference is 176, and the quotient is 93.</p>
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<p><strong>Step 7:</strong>Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeros to the dividend. Now the new dividend is 17600.</p>
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<p><strong>Step 7:</strong>Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeros to the dividend. Now the new dividend is 17600.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor, which is 939. We need to find n such that 939n x n is closest to 17600.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor, which is 939. We need to find n such that 939n x n is closest to 17600.</p>
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<p><strong>Step 9:</strong>Continuing this process will give us the approximate value of the square root of 8825.</p>
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<p><strong>Step 9:</strong>Continuing this process will give us the approximate value of the square root of 8825.</p>
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<h2>Square Root of 8825 by Approximation Method</h2>
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<h2>Square Root of 8825 by Approximation Method</h2>
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<p>The approximation method is another method for finding square roots. It is an easy method to estimate the square root of a given number. Now let us learn how to find the square root of 8825 using the approximation method.</p>
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<p>The approximation method is another method for finding square roots. It is an easy method to estimate the square root of a given number. Now let us learn how to find the square root of 8825 using the approximation method.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect squares around √8825. The smallest perfect square less than 8825 is 8836, and the largest perfect square<a>greater than</a>8825 is 8712. Therefore, √8825 falls somewhere between 93 and 94.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect squares around √8825. The smallest perfect square less than 8825 is 8836, and the largest perfect square<a>greater than</a>8825 is 8712. Therefore, √8825 falls somewhere between 93 and 94.</p>
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<p><strong>Step 2:</strong>Now we need to apply the<a>formula</a>: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) Going by the formula, (8825 - 8649) / (8836 - 8649) = 0.9685</p>
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<p><strong>Step 2:</strong>Now we need to apply the<a>formula</a>: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) Going by the formula, (8825 - 8649) / (8836 - 8649) = 0.9685</p>
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<p>Using the formula, we identified the<a>decimal</a>point of our square root. The next step is adding the value we got initially to the decimal number, which is 93 + 0.9685 = 93.9685. Thus, the square root of 8825 is approximately 93.9685.</p>
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<p>Using the formula, we identified the<a>decimal</a>point of our square root. The next step is adding the value we got initially to the decimal number, which is 93 + 0.9685 = 93.9685. Thus, the square root of 8825 is approximately 93.9685.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 8825</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 8825</h2>
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<p>Students often make mistakes while finding square roots, such as forgetting about the negative square root or skipping long division steps. Now let us look at a few of those mistakes that students tend to make in detail.</p>
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<p>Students often make mistakes while finding square roots, such as forgetting about the negative square root or skipping long division steps. Now let us look at a few of those mistakes that students tend to make in detail.</p>
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<h2>Download Worksheets</h2>
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<h3>Problem 1</h3>
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<h3>Problem 1</h3>
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<p>Can you help Max find the area of a square box if its side length is given as √8825?</p>
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<p>Can you help Max find the area of a square box if its side length is given as √8825?</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 8825 square units.</p>
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<p>The area of the square is 8825 square units.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>The area of the square = side^2.</p>
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<p>The area of the square = side^2.</p>
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<p>The side length is given as √8825.</p>
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<p>The side length is given as √8825.</p>
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<p>Area of the square = (√8825)^2 = 8825.</p>
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<p>Area of the square = (√8825)^2 = 8825.</p>
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<p>Therefore, the area of the square box is 8825 square units.</p>
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<p>Therefore, the area of the square box is 8825 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 8825 square feet is built; if each of the sides is √8825, what will be the square feet of half of the building?</p>
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<p>A square-shaped building measuring 8825 square feet is built; if each of the sides is √8825, 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>4412.5 square feet</p>
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<p>4412.5 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 8825 by 2 = 4412.5.</p>
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<p>Dividing 8825 by 2 = 4412.5.</p>
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<p>So half of the building measures 4412.5 square feet.</p>
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<p>So half of the building measures 4412.5 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 √8825 x 5.</p>
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<p>Calculate √8825 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>469.8425</p>
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<p>469.8425</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 8825, which is approximately 93.9685.</p>
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<p>The first step is to find the square root of 8825, which is approximately 93.9685.</p>
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<p>The second step is to multiply 93.9685 by 5.</p>
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<p>The second step is to multiply 93.9685 by 5.</p>
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<p>So, 93.9685 x 5 ≈ 469.8425.</p>
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<p>So, 93.9685 x 5 ≈ 469.8425.</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 (8825 + 25)?</p>
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<p>What will be the square root of (8825 + 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 95.</p>
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<p>The square root is 95.</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 (8825 + 25). 8825 + 25 = 8850, and then √8850 ≈ 94.12.</p>
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<p>To find the square root, we need to find the sum of (8825 + 25). 8825 + 25 = 8850, and then √8850 ≈ 94.12.</p>
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<p>Therefore, the square root of (8825 + 25) is approximately 94.12.</p>
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<p>Therefore, the square root of (8825 + 25) is approximately 94.12.</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 √8825 units and the width ‘w’ is 50 units.</p>
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<p>Find the perimeter of the rectangle if its length ‘l’ is √8825 units and the width ‘w’ is 50 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 approximately 387.937 units.</p>
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<p>The perimeter of the rectangle is approximately 387.937 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 × (√8825 + 50) = 2 × (93.9685 + 50) ≈ 2 × 143.9685 = 287.937 units.</p>
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<p>Perimeter = 2 × (√8825 + 50) = 2 × (93.9685 + 50) ≈ 2 × 143.9685 = 287.937 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 8825</h2>
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<h2>FAQ on Square Root of 8825</h2>
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<h3>1.What is √8825 in its simplest form?</h3>
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<h3>1.What is √8825 in its simplest form?</h3>
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<p>The prime factorization of 8825 is 5 x 5 x 7 x 13 x 19, so the simplest form of √8825 is √(5^2 x 7 x 13 x 19).</p>
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<p>The prime factorization of 8825 is 5 x 5 x 7 x 13 x 19, so the simplest form of √8825 is √(5^2 x 7 x 13 x 19).</p>
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<h3>2.Mention the factors of 8825.</h3>
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<h3>2.Mention the factors of 8825.</h3>
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<p>Factors of 8825 are 1, 5, 25, 7, 35, 49, 91, 245, 455, 637, 3185, and 8825.</p>
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<p>Factors of 8825 are 1, 5, 25, 7, 35, 49, 91, 245, 455, 637, 3185, and 8825.</p>
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<h3>3.Calculate the square of 8825.</h3>
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<h3>3.Calculate the square of 8825.</h3>
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<p>We get the square of 8825 by multiplying the number by itself, that is 8825 x 8825 = 77,914,625.</p>
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<p>We get the square of 8825 by multiplying the number by itself, that is 8825 x 8825 = 77,914,625.</p>
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<h3>4.Is 8825 a prime number?</h3>
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<h3>4.Is 8825 a prime number?</h3>
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<p>8825 is not a<a>prime number</a>, as it has more than two factors.</p>
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<p>8825 is not a<a>prime number</a>, as it has more than two factors.</p>
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<h3>5.8825 is divisible by?</h3>
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<h3>5.8825 is divisible by?</h3>
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<p>8825 has several factors; those are 1, 5, 25, 7, 35, 49, 91, 245, 455, 637, 3185, and 8825.</p>
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<p>8825 has several factors; those are 1, 5, 25, 7, 35, 49, 91, 245, 455, 637, 3185, and 8825.</p>
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<h2>Important Glossaries for the Square Root of 8825</h2>
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<h2>Important Glossaries for the Square Root of 8825</h2>
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<ul><li><strong>Square root:</strong>A square root is the inverse operation of squaring a number. For example, 4^2 = 16, and the square root is √16 = 4. </li>
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<ul><li><strong>Square root:</strong>A square root is the inverse operation of squaring a number. For example, 4^2 = 16, and the square root is √16 = 4. </li>
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<li><strong>Irrational number:</strong>An irrational number cannot be expressed in the form of p/q, where p and q are integers and q ≠ 0. </li>
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<li><strong>Irrational number:</strong>An irrational number cannot be expressed in the form of p/q, where p and q are integers and q ≠ 0. </li>
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<li><strong>Long division method:</strong>A method used for finding the square roots of non-perfect squares through a systematic approach of division. </li>
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<li><strong>Long division method:</strong>A method used for finding the square roots of non-perfect squares through a systematic approach of division. </li>
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<li><strong>Approximation:</strong>A method of estimating a value between two known values. </li>
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<li><strong>Approximation:</strong>A method of estimating a value between two known values. </li>
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<li><strong>Decimal:</strong>A number that includes a whole number and a fractional part, represented with a decimal point, such as 7.86, 8.65, and 9.42.</li>
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<li><strong>Decimal:</strong>A number that includes a whole number and a fractional part, represented with a decimal point, such as 7.86, 8.65, and 9.42.</li>
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</ul><p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>
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</ul><p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>
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<p>▶</p>
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<h2>Jaskaran Singh Saluja</h2>
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<h2>Jaskaran Singh Saluja</h2>
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<h3>About the Author</h3>
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<h3>About the Author</h3>
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<p>Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.</p>
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<p>Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.</p>
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<h3>Fun Fact</h3>
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<h3>Fun Fact</h3>
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<p>: He loves to play the quiz with kids through algebra to make kids love it.</p>
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<p>: He loves to play the quiz with kids through algebra to make kids love it.</p>