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2026-01-01
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2026-02-28
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<p>225 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 a square is a square root. The square root is used in various fields, including vehicle design and finance. Here, we will discuss the square root of 6250.</p>
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<p>If a number is multiplied by itself, the result is a square. The inverse of a square is a square root. The square root is used in various fields, including vehicle design and finance. Here, we will discuss the square root of 6250.</p>
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<h2>What is the Square Root of 6250?</h2>
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<h2>What is the Square Root of 6250?</h2>
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<p>The<a>square</a>root is the inverse<a>of</a>squaring a<a>number</a>. 6250 is not a<a>perfect square</a>. The square root of 6250 is expressed in both radical and exponential forms. In radical form, it is expressed as √6250, whereas in<a>exponential form</a>, it is (6250)^(1/2). √6250 ≈ 79.05694, which is an<a>irrational number</a>because it cannot be expressed as a<a>ratio</a>of two integers.</p>
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<p>The<a>square</a>root is the inverse<a>of</a>squaring a<a>number</a>. 6250 is not a<a>perfect square</a>. The square root of 6250 is expressed in both radical and exponential forms. In radical form, it is expressed as √6250, whereas in<a>exponential form</a>, it is (6250)^(1/2). √6250 ≈ 79.05694, which is an<a>irrational number</a>because it cannot be expressed as a<a>ratio</a>of two integers.</p>
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<h2>Finding the Square Root of 6250</h2>
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<h2>Finding the Square Root of 6250</h2>
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<p>The<a>prime factorization</a>method is used for perfect square numbers. For non-perfect square numbers like 6250, 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 like 6250, 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 6250 by Prime Factorization Method</h2>
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</ul><h2>Square Root of 6250 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 6250 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 6250 is broken down into its prime factors:</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 6250. Breaking it down, we get 2 x 5 x 5 x 5 x 5 x 5 x 5 x 5 = 2 x 5^4 x 5^2.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 6250. Breaking it down, we get 2 x 5 x 5 x 5 x 5 x 5 x 5 x 5 = 2 x 5^4 x 5^2.</p>
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<p><strong>Step 2:</strong>Now that we have found the prime factors of 6250, the second step is to form pairs of those prime factors. Since 6250 is not a perfect square, the digits of the number can’t be grouped into complete pairs, making it challenging to calculate the exact<a>square root</a>using prime factorization alone.</p>
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<p><strong>Step 2:</strong>Now that we have found the prime factors of 6250, the second step is to form pairs of those prime factors. Since 6250 is not a perfect square, the digits of the number can’t be grouped into complete pairs, making it challenging to calculate the exact<a>square root</a>using prime factorization alone.</p>
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<h2>Square Root of 6250 by Long Division Method</h2>
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<h2>Square Root of 6250 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 square root 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 square root using the long division method, step by step:</p>
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<p><strong>Step 1:</strong>To begin, we need to group the numbers from right to left. In the case of 6250, we need to group it as 50 and 62.</p>
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<p><strong>Step 1:</strong>To begin, we need to group the numbers from right to left. In the case of 6250, we need to group it as 50 and 62.</p>
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<p><strong>Step 2:</strong>Identify the largest number whose square is<a>less than</a>or equal to 62. We can say this number is '7' because 7 x 7 = 49, which is less than 62. Now the<a>quotient</a>is 7, and after subtracting 49 from 62, the<a>remainder</a>is 13.</p>
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<p><strong>Step 2:</strong>Identify the largest number whose square is<a>less than</a>or equal to 62. We can say this number is '7' because 7 x 7 = 49, which is less than 62. Now the<a>quotient</a>is 7, and after subtracting 49 from 62, the<a>remainder</a>is 13.</p>
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<p><strong>Step 3:</strong>Bring down the next pair of digits, which is 50, making the new<a>dividend</a>1350. Add the old<a>divisor</a>to itself (7 + 7 = 14) to get the new divisor.</p>
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<p><strong>Step 3:</strong>Bring down the next pair of digits, which is 50, making the new<a>dividend</a>1350. Add the old<a>divisor</a>to itself (7 + 7 = 14) to get the new divisor.</p>
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<p><strong>Step 4:</strong>Find a digit 'n' such that 14n x n is less than or equal to 1350. Let us consider n as 9, then 149 x 9 = 1341.</p>
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<p><strong>Step 4:</strong>Find a digit 'n' such that 14n x n is less than or equal to 1350. Let us consider n as 9, then 149 x 9 = 1341.</p>
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<p><strong>Step 5:</strong>Subtract 1341 from 1350; the difference is 9. The quotient now becomes 79.</p>
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<p><strong>Step 5:</strong>Subtract 1341 from 1350; the difference is 9. The quotient now becomes 79.</p>
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<p><strong>Step 6:</strong>Since the dividend is less than the divisor, we add a<a>decimal</a>point. Adding the decimal point allows us to add two zeroes to the dividend, making it 900.</p>
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<p><strong>Step 6:</strong>Since the dividend is less than the divisor, we add a<a>decimal</a>point. Adding the decimal point allows us to add two zeroes to the dividend, making it 900.</p>
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<p><strong>Step 7:</strong>Continue the process to find the next digit. The new divisor is 158, and since 158 x 5 = 790, the next digit in the quotient is 5.</p>
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<p><strong>Step 7:</strong>Continue the process to find the next digit. The new divisor is 158, and since 158 x 5 = 790, the next digit in the quotient is 5.</p>
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<p><strong>Step 8:</strong>Subtracting 790 from 900 gives 110. Continue this process until you achieve the desired precision.</p>
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<p><strong>Step 8:</strong>Subtracting 790 from 900 gives 110. Continue this process until you achieve the desired precision.</p>
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<p>So the square root of √6250 is approximately 79.056.</p>
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<p>So the square root of √6250 is approximately 79.056.</p>
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<h2>Square Root of 6250 by Approximation Method</h2>
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<h2>Square Root of 6250 by Approximation Method</h2>
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<p>The approximation method is another method for finding square roots; it is a straightforward method to estimate the square root of a given number. Now let us learn how to find the square root of 6250 using the approximation method.</p>
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<p>The approximation method is another method for finding square roots; it is a straightforward method to estimate the square root of a given number. Now let us learn how to find the square root of 6250 using the approximation method.</p>
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<p><strong>Step 1:</strong>Identify the closest perfect squares to √6250.</p>
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<p><strong>Step 1:</strong>Identify the closest perfect squares to √6250.</p>
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<p>The smallest perfect square less than 6250 is 6084, and the largest perfect square<a>greater than</a>6250 is 6400. Therefore, √6250 falls between 78 and 80.</p>
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<p>The smallest perfect square less than 6250 is 6084, and the largest perfect square<a>greater than</a>6250 is 6400. Therefore, √6250 falls between 78 and 80.</p>
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<p><strong>Step 2:</strong>Apply the<a>formula</a>: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula, (6250 - 6084) ÷ (6400 - 6084) ≈ 0.056. Add this decimal to the smaller<a>integer</a>root: 78 + 0.056 = 78.056.</p>
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<p><strong>Step 2:</strong>Apply the<a>formula</a>: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula, (6250 - 6084) ÷ (6400 - 6084) ≈ 0.056. Add this decimal to the smaller<a>integer</a>root: 78 + 0.056 = 78.056.</p>
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<p>Therefore, the square root of 6250 is approximately 79.056.</p>
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<p>Therefore, the square root of 6250 is approximately 79.056.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 6250</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 6250</h2>
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<p>Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Let us look at some 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 skipping steps in the long division method. Let us look at some common mistakes 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 √6250?</p>
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<p>Can you help Max find the area of a square box if its side length is given as √6250?</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 approximately 6250 square units.</p>
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<p>The area of the square is approximately 6250 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 = side^2.</p>
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<p>The area of a square = side^2.</p>
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<p>The side length is given as √6250.</p>
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<p>The side length is given as √6250.</p>
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<p>Area of the square = (√6250)^2 = 6250.</p>
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<p>Area of the square = (√6250)^2 = 6250.</p>
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<p>Therefore, the area of the square box is approximately 6250 square units.</p>
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<p>Therefore, the area of the square box is approximately 6250 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 plot measuring 6250 square feet is built; if each of the sides is √6250, what will be the square feet of half of the plot?</p>
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<p>A square-shaped plot measuring 6250 square feet is built; if each of the sides is √6250, what will be the square feet of half of the plot?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>3125 square feet</p>
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<p>3125 square feet</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>To find the area of half of the plot, divide the given area by 2.</p>
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<p>To find the area of half of the plot, divide the given area by 2.</p>
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<p>Dividing 6250 by 2 gives us 3125.</p>
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<p>Dividing 6250 by 2 gives us 3125.</p>
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<p>So, half of the plot measures 3125 square feet.</p>
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<p>So, half of the plot measures 3125 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 √6250 x 5.</p>
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<p>Calculate √6250 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>395.2847</p>
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<p>395.2847</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 6250, which is approximately 79.056.</p>
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<p>The first step is to find the square root of 6250, which is approximately 79.056.</p>
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<p>The second step is to multiply 79.056 by 5.</p>
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<p>The second step is to multiply 79.056 by 5.</p>
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<p>So, 79.056 x 5 ≈ 395.2847.</p>
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<p>So, 79.056 x 5 ≈ 395.2847.</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 (6250 + 150)?</p>
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<p>What will be the square root of (6250 + 150)?</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 approximately 80.</p>
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<p>The square root is approximately 80.</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, first find the sum of (6250 + 150). 6250 + 150 = 6400, and √6400 = 80.</p>
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<p>To find the square root, first find the sum of (6250 + 150). 6250 + 150 = 6400, and √6400 = 80.</p>
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<p>Therefore, the square root of (6250 + 150) is ±80.</p>
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<p>Therefore, the square root of (6250 + 150) is ±80.</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 √6250 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 √6250 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 258.1139 units.</p>
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<p>The perimeter of the rectangle is approximately 258.1139 units.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Perimeter of a rectangle = 2 × (length + width)</p>
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<p>Perimeter of a rectangle = 2 × (length + width)</p>
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<p>Perimeter = 2 × (√6250 + 50) ≈ 2 × (79.056 + 50) ≈ 2 × 129.056 ≈ 258.1139 units.</p>
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<p>Perimeter = 2 × (√6250 + 50) ≈ 2 × (79.056 + 50) ≈ 2 × 129.056 ≈ 258.1139 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 6250</h2>
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<h2>FAQ on Square Root of 6250</h2>
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<h3>1.What is √6250 in its simplest form?</h3>
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<h3>1.What is √6250 in its simplest form?</h3>
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<p>The prime factorization of 6250 is 2 x 5^4 x 5^2, so the simplest form of √6250 is √(2 x 5^6).</p>
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<p>The prime factorization of 6250 is 2 x 5^4 x 5^2, so the simplest form of √6250 is √(2 x 5^6).</p>
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<h3>2.Mention the factors of 6250.</h3>
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<h3>2.Mention the factors of 6250.</h3>
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<p>Factors of 6250 are 1, 2, 5, 10, 25, 50, 125, 250, 625, 1250, 3125, and 6250.</p>
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<p>Factors of 6250 are 1, 2, 5, 10, 25, 50, 125, 250, 625, 1250, 3125, and 6250.</p>
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<h3>3.Calculate the square of 6250.</h3>
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<h3>3.Calculate the square of 6250.</h3>
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<p>We get the square of 6250 by multiplying the number by itself: 6250 x 6250 = 39,062,500.</p>
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<p>We get the square of 6250 by multiplying the number by itself: 6250 x 6250 = 39,062,500.</p>
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<h3>4.Is 6250 a prime number?</h3>
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<h3>4.Is 6250 a prime number?</h3>
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<p>6250 is not a<a>prime number</a>, as it has more than two factors.</p>
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<p>6250 is not a<a>prime number</a>, as it has more than two factors.</p>
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<h3>5.6250 is divisible by?</h3>
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<h3>5.6250 is divisible by?</h3>
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<p>6250 has several factors; these include 1, 2, 5, 10, 25, 50, 125, 250, 625, 1250, 3125, and 6250.</p>
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<p>6250 has several factors; these include 1, 2, 5, 10, 25, 50, 125, 250, 625, 1250, 3125, and 6250.</p>
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<h2>Important Glossaries for the Square Root of 6250</h2>
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<h2>Important Glossaries for the Square Root of 6250</h2>
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<ul><li><strong>Square root:</strong>A square root is the inverse of squaring a number. Example: 4^2 = 16 and the inverse of the square is the square root, which is √16 = 4.</li>
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<ul><li><strong>Square root:</strong>A square root is the inverse of squaring a number. Example: 4^2 = 16 and the inverse of the square is the square root, which is √16 = 4.</li>
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</ul><ul><li><strong>Irrational number:</strong>An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.</li>
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</ul><ul><li><strong>Irrational number:</strong>An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.</li>
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</ul><ul><li><strong>Perfect square:</strong>A number that is the square of an integer. Example: 36 is a perfect square because it is 6^2.</li>
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</ul><ul><li><strong>Perfect square:</strong>A number that is the square of an integer. Example: 36 is a perfect square because it is 6^2.</li>
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</ul><ul><li><strong>Decimal:</strong>If a number has both a whole number and a fractional part, it is called a decimal. Examples: 7.86, 8.65, and 9.42.</li>
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</ul><ul><li><strong>Decimal:</strong>If a number has both a whole number and a fractional part, it is called a decimal. Examples: 7.86, 8.65, and 9.42.</li>
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</ul><ul><li><strong>Prime factorization:</strong>The expression of a number as a product of prime numbers. For example, the prime factorization of 50 is 2 x 5^2.</li>
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</ul><ul><li><strong>Prime factorization:</strong>The expression of a number as a product of prime numbers. For example, the prime factorization of 50 is 2 x 5^2.</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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<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>