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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 801, we need to group it as 01 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 801, we need to group it as 01 and 8.</p>
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<p><strong>Step 2:</strong>Now we need to find a number n whose square is<a>less than</a>or equal to 8. We choose n = 2 because 2 x 2 = 4, which is less than 8. The<a>quotient</a>is 2, and the<a>remainder</a>is 4 after subtracting 4 from 8.</p>
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<p><strong>Step 2:</strong>Now we need to find a number n whose square is<a>less than</a>or equal to 8. We choose n = 2 because 2 x 2 = 4, which is less than 8. The<a>quotient</a>is 2, and the<a>remainder</a>is 4 after subtracting 4 from 8.</p>
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<p><strong>Step 3:</strong>Bring down the next pair, which is 01, making the new<a>dividend</a>401.</p>
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<p><strong>Step 3:</strong>Bring down the next pair, which is 01, making the new<a>dividend</a>401.</p>
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<p><strong>Step 4:</strong>Double the quotient (2), giving us 4, and use it to find a new<a>divisor</a>. Consider 4n as the new divisor, and find n such that 4n x n ≤ 401.</p>
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<p><strong>Step 4:</strong>Double the quotient (2), giving us 4, and use it to find a new<a>divisor</a>. Consider 4n as the new divisor, and find n such that 4n x n ≤ 401.</p>
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<p><strong>Step 5:</strong>By trial, we find that n = 7 works, since 47 x 7 = 329.</p>
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<p><strong>Step 5:</strong>By trial, we find that n = 7 works, since 47 x 7 = 329.</p>
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<p><strong>Step 6:</strong>Subtract 329 from 401 to get a remainder of 72, and the quotient becomes 27.</p>
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<p><strong>Step 6:</strong>Subtract 329 from 401 to get a remainder of 72, and the quotient becomes 27.</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 a decimal point allows us to add two zeroes to the dividend, making it 7200.</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 a decimal point allows us to add two zeroes to the dividend, making it 7200.</p>
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<p><strong>Step 8:</strong>Find a new divisor by considering 54 (double the new quotient 27) and find n such that 54n x n ≤ 7200. With n = 1, 541 x 1 = 541.</p>
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<p><strong>Step 8:</strong>Find a new divisor by considering 54 (double the new quotient 27) and find n such that 54n x n ≤ 7200. With n = 1, 541 x 1 = 541.</p>
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<p><strong>Step 9:</strong>Subtract 541 from 7200 to get a remainder of 6659.</p>
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<p><strong>Step 9:</strong>Subtract 541 from 7200 to get a remainder of 6659.</p>
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<p><strong>Step 10:</strong>The quotient is now approximately 28.301. Continue with these steps until you get the desired precision.</p>
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<p><strong>Step 10:</strong>The quotient is now approximately 28.301. Continue with these steps until you get the desired precision.</p>
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<p>So the square root of √801 ≈ 28.3019.</p>
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<p>So the square root of √801 ≈ 28.3019.</p>
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