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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 1492, we need to group it as 92 and 14.</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 1492, we need to group it as 92 and 14.</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 14. We can say n as ‘3’ because 3 x 3 = 9, which is less than 14. Now the<a>quotient</a>is 3, and after subtracting 9 from 14, the<a>remainder</a>is 5.</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 14. We can say n as ‘3’ because 3 x 3 = 9, which is less than 14. Now the<a>quotient</a>is 3, and after subtracting 9 from 14, the<a>remainder</a>is 5.</p>
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<p><strong>Step 3:</strong>Now let us bring down 92, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number, 3 + 3 = 6, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 92, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number, 3 + 3 = 6, which will be our new divisor.</p>
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<p><strong>Step 4:</strong>The new divisor will be 6n. We need to find the value of n.</p>
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<p><strong>Step 4:</strong>The new divisor will be 6n. We need to find the value of n.</p>
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<p><strong>Step 5:</strong>The next step is finding 6n x n ≤ 592. Let us consider n as 9; now 69 x 9 = 621.</p>
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<p><strong>Step 5:</strong>The next step is finding 6n x n ≤ 592. Let us consider n as 9; now 69 x 9 = 621.</p>
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<p><strong>Step 6:</strong>Subtract 621 from 592; the difference is -29, indicating n was too large, so we try n = 8. Now 68 x 8 = 544.</p>
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<p><strong>Step 6:</strong>Subtract 621 from 592; the difference is -29, indicating n was too large, so we try n = 8. Now 68 x 8 = 544.</p>
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<p><strong>Step 7:</strong>Subtraction gives a remainder of 48, and the quotient is 38.</p>
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<p><strong>Step 7:</strong>Subtraction gives a remainder of 48, and the quotient is 38.</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 4800.</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 4800.</p>
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<p><strong>Step 9:</strong>Continue the long division steps to get an approximate square root value accurate to two decimal places.</p>
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<p><strong>Step 9:</strong>Continue the long division steps to get an approximate square root value accurate to two decimal places.</p>
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<p>So the square root of √1492 ≈ 38.63</p>
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<p>So the square root of √1492 ≈ 38.63</p>
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