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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 3121, we need to group it as 21 and 31.</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 3121, we need to group it as 21 and 31.</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 31. We can say n is 5 because 5 × 5 = 25 which is less than 31. Now the<a>quotient</a>is 5, and after subtracting 25 from 31, the<a>remainder</a>is 6.</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 31. We can say n is 5 because 5 × 5 = 25 which is less than 31. Now the<a>quotient</a>is 5, and after subtracting 25 from 31, the<a>remainder</a>is 6.</p>
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<p><strong>Step 3:</strong>Bring down 21 which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 5 + 5, we get 10 which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Bring down 21 which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 5 + 5, we get 10 which will be our new divisor.</p>
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<p><strong>Step 4:</strong>The new divisor will be the sum of the previous quotient and divisor. Now we get 10n 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 sum of the previous quotient and divisor. Now we get 10n 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 10n × n ≤ 621. Let us consider n as 5, now 105 × 5 = 525.</p>
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<p><strong>Step 5</strong>: The next step is finding 10n × n ≤ 621. Let us consider n as 5, now 105 × 5 = 525.</p>
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<p><strong>Step 6:</strong>Subtract 621 from 525, the difference is 96, and the quotient is 55.</p>
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<p><strong>Step 6:</strong>Subtract 621 from 525, the difference is 96, and the quotient is 55.</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 zeros to the dividend. Now the new dividend is 9600.</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 zeros to the dividend. Now the new dividend is 9600.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 558 because 558 × 8 = 4464.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 558 because 558 × 8 = 4464.</p>
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<p><strong>Step 9:</strong>Subtracting 4464 from 9600 we get the result 5136.</p>
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<p><strong>Step 9:</strong>Subtracting 4464 from 9600 we get the result 5136.</p>
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<p><strong>Step 10:</strong>Now the quotient is 55.8.</p>
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<p><strong>Step 10:</strong>Now the quotient is 55.8.</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. So the square root of √3121 is approximately 55.83.</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. So the square root of √3121 is approximately 55.83.</p>
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