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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<a>square root</a>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<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 8192, we need to group it as 92 and 81.</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 8192, we need to group it as 92 and 81.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is closest to 81. We can say n as ‘9’ because 9 x 9 = 81 is lesser than or equal to 81. Now the<a>quotient</a>is 9, and after subtracting 81-81 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 closest to 81. We can say n as ‘9’ because 9 x 9 = 81 is lesser than or equal to 81. Now the<a>quotient</a>is 9, and after subtracting 81-81 the<a>remainder</a>is 0.</p>
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<p><strong>Step 3:</strong>Now let us bring down 92, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number, 9 + 9 = 18, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 92, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number, 9 + 9 = 18, 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 18n 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 18n 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 18n x n ≤ 9200. Let us consider n as 5, now 185 x 5 = 925.</p>
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<p><strong>Step 5:</strong>The next step is finding 18n x n ≤ 9200. Let us consider n as 5, now 185 x 5 = 925.</p>
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<p><strong>Step 6:</strong>Subtract 9200 from 925, the difference is 8275, and the new quotient is 90.5.</p>
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<p><strong>Step 6:</strong>Subtract 9200 from 925, the difference is 8275, and the new quotient is 90.5.</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 827500.</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 827500.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 180 because 18005 x 5 = 90025.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 180 because 18005 x 5 = 90025.</p>
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<p><strong>Step 9:</strong>Subtracting 90025 from 827500, we get the result 737475.</p>
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<p><strong>Step 9:</strong>Subtracting 90025 from 827500, we get the result 737475.</p>
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<p><strong>Step 10:</strong>Now the quotient is 90.50.</p>
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<p><strong>Step 10:</strong>Now the quotient is 90.50.</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 until the remainder is zero. So the square root of √8192 is approximately 90.51.</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 until the remainder is zero. So the square root of √8192 is approximately 90.51.</p>
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