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Original
2026-01-01
Modified
2026-02-28
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<p>The<a>long division</a>method is particularly used for non-perfect square numbers. In this method, we 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<a>long division</a>method is particularly used for non-perfect square numbers. In this method, we 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 with, we need to group the numbers from right to left. In the case of 831, we need to group it as 31 and 8.</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 831, we need to group it as 31 and 8.</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 8. We can say n is ‘2’ because 2 x 2 = 4, which is less than 8. Now the<a>quotient</a>is 2. After subtracting 4 from 8, the<a>remainder</a>is 4.</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 8. We can say n is ‘2’ because 2 x 2 = 4, which is less than 8. Now the<a>quotient</a>is 2. After subtracting 4 from 8, the<a>remainder</a>is 4.</p>
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<p><strong>Step 3:</strong>Now let us bring down 31, making the new<a>dividend</a>431. Add the old<a>divisor</a>with the same number: 2 + 2 = 4, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 31, making the new<a>dividend</a>431. Add the old<a>divisor</a>with the same number: 2 + 2 = 4, which will be our new divisor.</p>
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<p><strong>Step 4:</strong>The new divisor will be 4n. We need to find the value of n such that 4n x n ≤ 431.</p>
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<p><strong>Step 4:</strong>The new divisor will be 4n. We need to find the value of n such that 4n x n ≤ 431.</p>
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<p><strong>Step 5:</strong>The next step is finding 4n x n ≤ 431. Let n be 7, now 47 x 7 = 329.</p>
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<p><strong>Step 5:</strong>The next step is finding 4n x n ≤ 431. Let n be 7, now 47 x 7 = 329.</p>
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<p><strong>Step 6:</strong>Subtract 329 from 431. The difference is 102, and the quotient is 27.</p>
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<p><strong>Step 6:</strong>Subtract 329 from 431. The difference is 102, and the quotient is 27.</p>
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<p><strong>Step 7:</strong>Since the dividend is less than the divisor, we need to add a<a>decimal</a>point. Adding the decimal point allows us to add two zeroes to the dividend. The new dividend is 10200.</p>
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<p><strong>Step 7:</strong>Since the dividend is less than the divisor, we need to add a<a>decimal</a>point. Adding the decimal point allows us to add two zeroes to the dividend. The new dividend is 10200.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor. The trial divisor is 554 because 554 x 18 = 9972.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor. The trial divisor is 554 because 554 x 18 = 9972.</p>
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<p><strong>Step 9:</strong>Subtracting 9972 from 10200, we get 228.</p>
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<p><strong>Step 9:</strong>Subtracting 9972 from 10200, we get 228.</p>
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<p><strong>Step 10:</strong>Now the quotient is 28.8.</p>
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<p><strong>Step 10:</strong>Now the quotient is 28.8.</p>
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<p><strong>Step 11:</strong>Continue doing these steps until we get two numbers after the decimal point. If there are no decimal values, continue till the remainder is zero.</p>
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<p><strong>Step 11:</strong>Continue doing these steps until we get two numbers after the decimal point. If there are no decimal values, continue till the remainder is zero.</p>
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<p>So the square root of √831 is approximately 28.83.</p>
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<p>So the square root of √831 is approximately 28.83.</p>
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