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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 865, we need to group it as 65 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 865, we need to group it as 65 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, which is less than 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<a>less than</a>or equal to 8. We can say n is 2 because 2 × 2 = 4, which is less than 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 65, which makes the new<a>dividend</a>465. Add the old<a>divisor</a>with the same number, 2 + 2, to get 4, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 65, which makes the new<a>dividend</a>465. Add the old<a>divisor</a>with the same number, 2 + 2, to get 4, which will be our new divisor.</p>
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<p><strong>Step 4:</strong>The new divisor is 4n. We need to find n such that 4n × n ≤ 465. Let n be 9; then, 49 × 9 = 441.</p>
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<p><strong>Step 4:</strong>The new divisor is 4n. We need to find n such that 4n × n ≤ 465. Let n be 9; then, 49 × 9 = 441.</p>
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<p><strong>Step 5:</strong>Subtract 441 from 465; the difference is 24, and the quotient is 29.</p>
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<p><strong>Step 5:</strong>Subtract 441 from 465; the difference is 24, and the quotient is 29.</p>
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<p><strong>Step 6:</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 2400.</p>
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<p><strong>Step 6:</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 2400.</p>
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<p><strong>Step 7:</strong>Now we need to find the new divisor, which is 8 because 298 × 8 = 2384.</p>
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<p><strong>Step 7:</strong>Now we need to find the new divisor, which is 8 because 298 × 8 = 2384.</p>
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<p><strong>Step 8:</strong>Subtracting 2384 from 2400, we get the result 16.</p>
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<p><strong>Step 8:</strong>Subtracting 2384 from 2400, we get the result 16.</p>
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<p><strong>Step 9:</strong>Now the quotient is 29.4.</p>
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<p><strong>Step 9:</strong>Now the quotient is 29.4.</p>
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<p><strong>Step 10:</strong>Continue doing these steps until we get two numbers after the decimal point or until the remainder is zero.</p>
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<p><strong>Step 10:</strong>Continue doing these steps until we get two numbers after the decimal point or until the remainder is zero.</p>
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<p>So the square root of √865 is approximately 29.41.</p>
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<p>So the square root of √865 is approximately 29.41.</p>
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