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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 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<a>long 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 with, we need to group the numbers from right to left. In the case of 108, we need to group it as 08 and 1.</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 108, we need to group it as 08 and 1.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is 1. We can say n as ‘1’ because 1 x 1 is lesser than or equal to 1. Now the<a>quotient</a>is 1, and after subtracting 1-1, the<a>remainder</a>is 0.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is 1. We can say n as ‘1’ because 1 x 1 is lesser than or equal to 1. Now the<a>quotient</a>is 1, and after subtracting 1-1, the<a>remainder</a>is 0.</p>
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<p><strong>Step 3:</strong>Now let us bring down 08, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number, 1 + 1, we get 2, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 08, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number, 1 + 1, we get 2, which will be our new divisor.</p>
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<p><strong>Step 4:</strong>The new divisor will be the<a>sum</a>of the dividend and quotient. Now we get 2n as the new divisor, and we need to find the value of n.</p>
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<p><strong>Step 4:</strong>The new divisor will be the<a>sum</a>of the dividend and quotient. Now we get 2n as the new divisor, and we need to find the value of n.</p>
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<p><strong>Step 5:</strong>The next step is finding 2n × n ≤ 08. Let us consider n as 4, now 2 x 4 x 4 = 64.</p>
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<p><strong>Step 5:</strong>The next step is finding 2n × n ≤ 08. Let us consider n as 4, now 2 x 4 x 4 = 64.</p>
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<p><strong>Step 6:</strong>Subtract 08 from 64; the difference is 44, and the quotient is 10.4.</p>
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<p><strong>Step 6:</strong>Subtract 08 from 64; the difference is 44, and the quotient is 10.4.</p>
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<p><strong>Step 7:</strong>Since the dividend is<a>less than</a>the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 4400.</p>
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<p><strong>Step 7:</strong>Since the dividend is<a>less than</a>the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 4400.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor, which is 9, because 209 x 9 = 1881.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor, which is 9, because 209 x 9 = 1881.</p>
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<p><strong>Step 9:</strong>Subtracting 1881 from 4400, we get the result 2519.</p>
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<p><strong>Step 9:</strong>Subtracting 1881 from 4400, we get the result 2519.</p>
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<p><strong>Step 10:</strong>Now the quotient is 10.39.</p>
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<p><strong>Step 10:</strong>Now the quotient is 10.39.</p>
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<p><strong>Step 11:</strong>Continue doing these steps until we get two numbers after the decimal point. Suppose 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. Suppose there are no decimal values; continue till the remainder is zero.</p>
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<p>So the square root of √108 is 10.39.</p>
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<p>So the square root of √108 is 10.39.</p>
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