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Original
2026-01-01
Modified
2026-02-28
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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 105, we need to group it as 05 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 105, we need to group it as 05 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 is ‘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 is ‘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 05, 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 05, 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, 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, we need to find the value of n.</p>
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<p><strong>Step 5:</strong>The next step is finding 2n x n ≤ 05. Since 2 x 1 x 1 = 2, it's not possible. We continue with 2 x 0 x 0 = 0.</p>
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<p><strong>Step 5:</strong>The next step is finding 2n x n ≤ 05. Since 2 x 1 x 1 = 2, it's not possible. We continue with 2 x 0 x 0 = 0.</p>
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<p><strong>Step 6:</strong>Subtract 05 from 0, the difference is 5, and the quotient is 10.</p>
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<p><strong>Step 6:</strong>Subtract 05 from 0, the difference is 5, and the quotient is 10.</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 zeroes to the dividend. Now the new dividend is 500.</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 zeroes to the dividend. Now the new dividend is 500.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 20 because 202 x 2 = 404. Step 9: Subtracting 404 from 500, we get the result 96.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 20 because 202 x 2 = 404. Step 9: Subtracting 404 from 500, we get the result 96.</p>
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<p><strong>Step 10:</strong>Now the quotient is 10.2.</p>
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<p><strong>Step 10:</strong>Now the quotient is 10.2.</p>
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<p><strong>Step 11:</strong>Continue doing these steps until we get two numbers after the decimal point. Suppose 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. Suppose if there are no decimal values, continue till the remainder is zero.</p>
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<p>So the square root of √105 is approximately 10.25.</p>
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<p>So the square root of √105 is approximately 10.25.</p>
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