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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 113, we need to group it as 13 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 113, we need to group it as 13 and 1.</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 1. We can say n as '1' because 1 × 1 is less than or equal to 1. Now the<a>quotient</a>is 1, and the<a>remainder</a>is 0 after subtracting 1 from 1.</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 1. We can say n as '1' because 1 × 1 is less than or equal to 1. Now the<a>quotient</a>is 1, and the<a>remainder</a>is 0 after subtracting 1 from 1.</p>
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<p><strong>Step 3:</strong>Bring down 13, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number, 1 + 1, to get 2, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Bring down 13, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number, 1 + 1, to get 2, 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 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 sum 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 ≤ 13. Let us consider n as 6, now 26 × 6 = 156.</p>
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<p><strong>Step 5:</strong>The next step is finding 2n × n ≤ 13. Let us consider n as 6, now 26 × 6 = 156.</p>
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<p><strong>Step 6:</strong>Since 156 is greater than 13, we try n as 5, so 25 × 5 = 125, which is still greater. We try n as 4, so 24 × 4 = 96, which is less than 113.</p>
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<p><strong>Step 6:</strong>Since 156 is greater than 13, we try n as 5, so 25 × 5 = 125, which is still greater. We try n as 4, so 24 × 4 = 96, which is less than 113.</p>
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<p><strong>Step 7</strong>: Subtract 96 from 113 to get the difference, which is 17. The quotient is 10.6.</p>
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<p><strong>Step 7</strong>: Subtract 96 from 113 to get the difference, which is 17. The quotient is 10.6.</p>
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<p><strong>Step 8:</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 1700.</p>
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<p><strong>Step 8:</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 1700.</p>
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<p><strong>Step 9:</strong>Continue this process until you reach the desired precision. The square root of √113 is approximately 10.63.</p>
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<p><strong>Step 9:</strong>Continue this process until you reach the desired precision. The square root of √113 is approximately 10.63.</p>
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