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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 869, we need to group it as 69 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 869, we need to group it as 69 and 8.</p>
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<p><strong>Step 2:</strong>Now, we need to find n whose square is ≤ 8. We can say n as ‘2’ because 2 x 2 = 4, which is lesser than or equal to 8. Now the<a>quotient</a>is 2, and after subtracting 4 from 8, 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 ≤ 8. We can say n as ‘2’ because 2 x 2 = 4, which is lesser than or equal to 8. Now the<a>quotient</a>is 2, and after subtracting 4 from 8, the<a>remainder</a>is 4.</p>
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<p><strong>Step 3:</strong>Now, let us bring down 69, 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>Now, let us bring down 69, 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<a>sum</a>of the dividend and quotient. Now we get 4n as the new divisor, and we need to find the value of n.</p>
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<p><strong>Step 4:</strong>The new divisor will be the<a>sum</a>of the dividend and quotient. Now we get 4n as the new divisor, and 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 ≤ 469. Let us consider n as 1, now 41 x 1 = 41.</p>
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<p><strong>Step 5:</strong>The next step is finding 4n × n ≤ 469. Let us consider n as 1, now 41 x 1 = 41.</p>
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<p><strong>Step 6:</strong>Subtract 41 from 46, the difference is 5, and the quotient is 21.</p>
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<p><strong>Step 6:</strong>Subtract 41 from 46, the difference is 5, and the quotient is 21.</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 500.</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 500.</p>
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<p><strong>Step 8:</strong>Now, we need to find the new divisor that is 294 because 294 x 1 = 294.</p>
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<p><strong>Step 8:</strong>Now, we need to find the new divisor that is 294 because 294 x 1 = 294.</p>
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<p><strong>Step 9:</strong>Subtracting 294 from 500, we get the result 206.</p>
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<p><strong>Step 9:</strong>Subtracting 294 from 500, we get the result 206.</p>
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<p><strong>Step 10:</strong>Now, the quotient is 29.4.</p>
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<p><strong>Step 10:</strong>Now, the quotient is 29.4.</p>
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<p><strong>Step 11:</strong>Continue doing these steps until we get two numbers after the decimal point. If there are no decimal values, continue until the remainder is zero.</p>
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<p><strong>Step 11:</strong>Continue doing these steps until we get two numbers after the decimal point. If there are no decimal values, continue until the remainder is zero.</p>
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<p>So the square root of √869 ≈ 29.48</p>
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<p>So the square root of √869 ≈ 29.48</p>
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