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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 53.21, we treat it as 53 and 21.</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 53.21, we treat it as 53 and 21.</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 53. We can say n is 7 because 7 x 7 = 49, which is less than 53.</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 53. We can say n is 7 because 7 x 7 = 49, which is less than 53.</p>
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<p><strong>Step 3:</strong>Subtract 49 from 53, and the<a>remainder</a>is 4. Bring down the 21, making it 421.</p>
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<p><strong>Step 3:</strong>Subtract 49 from 53, and the<a>remainder</a>is 4. Bring down the 21, making it 421.</p>
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<p><strong>Step 4:</strong>Double the<a>quotient</a>obtained in Step 2, which is 7, to get 14.</p>
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<p><strong>Step 4:</strong>Double the<a>quotient</a>obtained in Step 2, which is 7, to get 14.</p>
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<p><strong>Step 5:</strong>Now, determine a digit x such that 14x * x ≤ 421. The value of x is 2, because 142 * 2 = 284.</p>
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<p><strong>Step 5:</strong>Now, determine a digit x such that 14x * x ≤ 421. The value of x is 2, because 142 * 2 = 284.</p>
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<p><strong>Step 6:</strong>Subtract 284 from 421 to get a remainder of 137.</p>
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<p><strong>Step 6:</strong>Subtract 284 from 421 to get a remainder of 137.</p>
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<p><strong>Step 7:</strong>Since the remainder is less than the<a>divisor</a>, add a<a>decimal</a>point and bring down two zeros, making it 13700.</p>
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<p><strong>Step 7:</strong>Since the remainder is less than the<a>divisor</a>, add a<a>decimal</a>point and bring down two zeros, making it 13700.</p>
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<p><strong>Step 8:</strong>The new divisor is 144 (142 plus 2), and find x such that 144x * x ≤ 13700. After iterations, the value of x is found to be 9.</p>
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<p><strong>Step 8:</strong>The new divisor is 144 (142 plus 2), and find x such that 144x * x ≤ 13700. After iterations, the value of x is found to be 9.</p>
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<p><strong>Step 9:</strong>Subtract and continue the process to find more decimal places as needed.</p>
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<p><strong>Step 9:</strong>Subtract and continue the process to find more decimal places as needed.</p>
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<p>So the square root of √53.21 is approximately 7.296.</p>
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<p>So the square root of √53.21 is approximately 7.296.</p>
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