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Original
2026-01-01
Modified
2026-02-28
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<p>The long<a>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 long<a>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 514, we need to group it as 14 and 5.</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 514, we need to group it as 14 and 5.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is closest to 5 without exceeding it. We can say n as ‘2’ because 2 x 2 = 4, which is<a>less than</a>or equal to 5. Now the<a>quotient</a>is 2. After subtracting 4 from 5, the<a>remainder</a>is 1.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is closest to 5 without exceeding it. We can say n as ‘2’ because 2 x 2 = 4, which is<a>less than</a>or equal to 5. Now the<a>quotient</a>is 2. After subtracting 4 from 5, the<a>remainder</a>is 1.</p>
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<p><strong>Step 3:</strong>Bring down 14, making the new<a>dividend</a>114. Add the old<a>divisor</a>with the same number 2 + 2 = 4, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Bring down 14, making the new<a>dividend</a>114. Add the old<a>divisor</a>with the same number 2 + 2 = 4, which will be our new divisor.</p>
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<p><strong>Step 4:</strong>Find the value of n such that 4n x n ≤ 114. Let n = 2, so 42 x 2 = 84.</p>
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<p><strong>Step 4:</strong>Find the value of n such that 4n x n ≤ 114. Let n = 2, so 42 x 2 = 84.</p>
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<p><strong>Step 5:</strong>Subtract 84 from 114, the difference is 30, and the quotient is 22.</p>
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<p><strong>Step 5:</strong>Subtract 84 from 114, the difference is 30, and the quotient is 22.</p>
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<p><strong>Step 6:</strong>Since the dividend is less than the divisor, we need to add a<a>decimal</a>point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 3000.</p>
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<p><strong>Step 6:</strong>Since the dividend is less than the divisor, we need to add a<a>decimal</a>point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 3000.</p>
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<p><strong>Step 7:</strong>The next step is finding the new divisor. Try n = 7, as 447 x 7 = 3129, which exceeds 3000. Try n = 6, as 446 x 6 = 2676.</p>
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<p><strong>Step 7:</strong>The next step is finding the new divisor. Try n = 7, as 447 x 7 = 3129, which exceeds 3000. Try n = 6, as 446 x 6 = 2676.</p>
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<p><strong>Step 8:</strong>Subtracting 2676 from 3000 gives 324.</p>
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<p><strong>Step 8:</strong>Subtracting 2676 from 3000 gives 324.</p>
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<p><strong>Step 9:</strong>The quotient is approximately 22.67. Continue the process to obtain more decimal places if necessary.</p>
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<p><strong>Step 9:</strong>The quotient is approximately 22.67. Continue the process to obtain more decimal places if necessary.</p>
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<p>So the square root of √514 is approximately 22.67157.</p>
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<p>So the square root of √514 is approximately 22.67157.</p>
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