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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<a>square root</a>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<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 565, we need to consider it as 65 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 565, we need to consider it as 65 and 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 5. We can say n is 2 because 2 × 2 = 4, which is less than 5. Now the<a>quotient</a>is 2, and after subtracting 5 - 4, 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<a>less than</a>or equal to 5. We can say n is 2 because 2 × 2 = 4, which is less than 5. Now the<a>quotient</a>is 2, and after subtracting 5 - 4, the<a>remainder</a>is 1.</p>
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<p><strong>Step 3:</strong>Bring down 65 to make it 165. 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>Bring down 65 to make it 165. 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 will be the<a>sum</a>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<a>sum</a>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 ≤ 165. Let us consider n as 3, now 4 × 3 × 3 = 144.</p>
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<p><strong>Step 5:</strong>The next step is finding 4n × n ≤ 165. Let us consider n as 3, now 4 × 3 × 3 = 144.</p>
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<p><strong>Step 6:</strong>Subtract 165 from 144, the difference is 21, and the quotient is 23.</p>
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<p><strong>Step 6:</strong>Subtract 165 from 144, the difference is 21, and the quotient is 23.</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 2100.</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 2100.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 474 because 474 × 4 = 1896.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 474 because 474 × 4 = 1896.</p>
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<p><strong>Step 9:</strong>Subtracting 1896 from 2100, we get the result 204.</p>
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<p><strong>Step 9:</strong>Subtracting 1896 from 2100, we get the result 204.</p>
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<p><strong>Step 10:</strong>Now the quotient is 23.7.</p>
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<p><strong>Step 10:</strong>Now the quotient is 23.7.</p>
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<p><strong>Step 11:</strong>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 11:</strong>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 √565 is approximately 23.74.</p>
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<p>So the square root of √565 is approximately 23.74.</p>
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