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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 square root 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 square root 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 813, we need to group it as 13 and 8.</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 813, we need to group it as 13 and 8.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is ≤ 8. We can say n is '2' because 2 × 2 = 4, which is<a>less than</a>or equal to 8. Now the<a>quotient</a>is 2, and after subtracting 4 from 8, the<a>remainder</a>is 4.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is ≤ 8. We can say n is '2' because 2 × 2 = 4, which is<a>less than</a>or equal to 8. Now the<a>quotient</a>is 2, and after subtracting 4 from 8, the<a>remainder</a>is 4.</p>
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<p><strong>Step 3:</strong>Bring down 13 to make the new<a>dividend</a>413.</p>
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<p><strong>Step 3:</strong>Bring down 13 to make the new<a>dividend</a>413.</p>
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<p><strong>Step 4:</strong>Double the current quotient to get our new<a>divisor</a>which becomes 4. Now we have to find a digit x such that 4x × x is less than or equal to 413.</p>
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<p><strong>Step 4:</strong>Double the current quotient to get our new<a>divisor</a>which becomes 4. Now we have to find a digit x such that 4x × x is less than or equal to 413.</p>
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<p><strong>Step 5:</strong>Trying x = 9, we find 49 × 9 = 441, which is more than 413. Trying x = 8, 48 × 8 = 384, which works. The new remainder is 413 - 384 = 29.</p>
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<p><strong>Step 5:</strong>Trying x = 9, we find 49 × 9 = 441, which is more than 413. Trying x = 8, 48 × 8 = 384, which works. The new remainder is 413 - 384 = 29.</p>
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<p><strong>Step 6:</strong>Since the dividend is less than the divisor, add a<a>decimal</a>point which allows us to add two zeroes to the dividend. The new dividend is 2900.</p>
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<p><strong>Step 6:</strong>Since the dividend is less than the divisor, add a<a>decimal</a>point which allows us to add two zeroes to the dividend. The new dividend is 2900.</p>
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<p><strong>Step 7:</strong>Now find the new divisor, which is 576, because 2856 × 6 = 2856, which is close to 2900.</p>
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<p><strong>Step 7:</strong>Now find the new divisor, which is 576, because 2856 × 6 = 2856, which is close to 2900.</p>
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<p><strong>Step 8:</strong>Subtract 2856 from 2900, resulting in 44.</p>
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<p><strong>Step 8:</strong>Subtract 2856 from 2900, resulting in 44.</p>
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<p><strong>Step 9:</strong>Continue doing these steps until the desired precision is achieved. The quotient becomes approximately 28.514.</p>
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<p><strong>Step 9:</strong>Continue doing these steps until the desired precision is achieved. The quotient becomes approximately 28.514.</p>
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