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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 829, we need to group it as 29 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 829, we need to group it as 29 and 8.</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 8. We can say n is ‘2’ because 2 * 2 = 4 is less than 8. Now the<a>quotient</a>is 2, and after subtracting 8 - 4, 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<a>less than</a>or equal to 8. We can say n is ‘2’ because 2 * 2 = 4 is less than 8. Now the<a>quotient</a>is 2, and after subtracting 8 - 4, the<a>remainder</a>is 4.</p>
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<p><strong>Step 3:</strong>Bring down 29, which is the new<a>dividend</a>. 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 29, which is the new<a>dividend</a>. 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>The new divisor will be the sum of the dividend and quotient. Now we get 4n as the new divisor, we need to find the value of n.</p>
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<p><strong>Step 4:</strong>The new divisor will be the sum of the dividend and quotient. Now we get 4n as the new divisor, we need to find the value of n.</p>
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<p><strong>Step 5:</strong>The next step is finding 4n × n ≤ 429. Let us consider n as 7, now 4 * 7 * 7 = 294.</p>
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<p><strong>Step 5:</strong>The next step is finding 4n × n ≤ 429. Let us consider n as 7, now 4 * 7 * 7 = 294.</p>
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<p><strong>Step 6:</strong>Subtract 429 - 294, the difference is 135, and the quotient is 27.</p>
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<p><strong>Step 6:</strong>Subtract 429 - 294, the difference is 135, and the quotient is 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 the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 13500.</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 the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 13500.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 54 because 547 × 7 = 3829.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 54 because 547 × 7 = 3829.</p>
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<p><strong>Step 9:</strong>Subtracting 3829 from 13500, we get the result 9671.</p>
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<p><strong>Step 9:</strong>Subtracting 3829 from 13500, we get the result 9671.</p>
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<p><strong>Step 10:</strong>Now the quotient is 28.7 Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero.</p>
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<p><strong>Step 10:</strong>Now the quotient is 28.7 Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero.</p>
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<p>So the square root of √829 is approximately 28.8.</p>
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<p>So the square root of √829 is approximately 28.8.</p>
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