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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, group the numbers from right to left. In the case of 34.57, consider it as 34 and 57.</p>
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<p><strong>Step 1:</strong>To begin with, group the numbers from right to left. In the case of 34.57, consider it as 34 and 57.</p>
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<p><strong>Step 2:</strong>Find n whose square is<a>less than</a>or equal to 34. We can say n is 5 because 5 × 5 = 25, which is less than 34. Now the<a>quotient</a>is 5, and after subtracting 25 from 34, the<a>remainder</a>is 9.</p>
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<p><strong>Step 2:</strong>Find n whose square is<a>less than</a>or equal to 34. We can say n is 5 because 5 × 5 = 25, which is less than 34. Now the<a>quotient</a>is 5, and after subtracting 25 from 34, the<a>remainder</a>is 9.</p>
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<p><strong>Step 3:</strong>Bring down 57, making it the new<a>dividend</a>957. Add the old<a>divisor</a>with the same number: 5 + 5 = 10, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Bring down 57, making it the new<a>dividend</a>957. Add the old<a>divisor</a>with the same number: 5 + 5 = 10, which will be our new divisor.</p>
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<p><strong>Step 4:</strong>The new divisor will be 10n. We need to find the value of n such that 10n × n is less than or equal to 957. Let n be 9, so 109 × 9 = 981. Since 981 is greater than 957, try n = 8, making 108 × 8 = 864.</p>
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<p><strong>Step 4:</strong>The new divisor will be 10n. We need to find the value of n such that 10n × n is less than or equal to 957. Let n be 9, so 109 × 9 = 981. Since 981 is greater than 957, try n = 8, making 108 × 8 = 864.</p>
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<p><strong>Step 5:</strong>Subtract 864 from 957; the difference is 93, and the quotient is 5.8.</p>
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<p><strong>Step 5:</strong>Subtract 864 from 957; the difference is 93, and the quotient is 5.8.</p>
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<p><strong>Step 6:</strong>Since the dividend is less than the divisor, add a decimal point, allowing us to add two zeroes to the dividend. The new dividend is 9300.</p>
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<p><strong>Step 6:</strong>Since the dividend is less than the divisor, add a decimal point, allowing us to add two zeroes to the dividend. The new dividend is 9300.</p>
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<p><strong>Step 7:</strong>Find the new divisor. 108n becomes 1088, and n is 8 because 1088 × 8 = 8704.</p>
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<p><strong>Step 7:</strong>Find the new divisor. 108n becomes 1088, and n is 8 because 1088 × 8 = 8704.</p>
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<p><strong>Step 8:</strong>Subtracting 8704 from 9300 gives the result of 596.</p>
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<p><strong>Step 8:</strong>Subtracting 8704 from 9300 gives the result of 596.</p>
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<p><strong>Step 9:</strong>Continue doing these steps until you get two numbers after the decimal point.</p>
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<p><strong>Step 9:</strong>Continue doing these steps until you get two numbers after the decimal point.</p>
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<p>So the square root of √34.57 is approximately 5.879.</p>
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<p>So the square root of √34.57 is approximately 5.879.</p>
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