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Original
2026-01-01
Modified
2026-02-21
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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 2005, we need to group it as 05 and 20.</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 2005, we need to group it as 05 and 20.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is closest to 20. We can say n is 4 because 4 x 4 = 16, which is lesser than or equal to 20. Now the<a>quotient</a>is 4, and the<a>remainder</a>is 20 - 16 = 4.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is closest to 20. We can say n is 4 because 4 x 4 = 16, which is lesser than or equal to 20. Now the<a>quotient</a>is 4, and the<a>remainder</a>is 20 - 16 = 4.</p>
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<p><strong>Step 3:</strong>Now let us bring down 05, giving us a new<a>dividend</a>of 405. Add the old<a>divisor</a>with the same number: 4 + 4 = 8, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 05, giving us a new<a>dividend</a>of 405. Add the old<a>divisor</a>with the same number: 4 + 4 = 8, which will be our new divisor.</p>
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<p><strong>Step 4:</strong>We need to find the largest possible digit x such that 8x * x ≤ 405. For x = 5, 85 * 5 = 425, which is more than 405. For x = 4, 84 * 4 = 336, which is<a>less than</a>405.</p>
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<p><strong>Step 4:</strong>We need to find the largest possible digit x such that 8x * x ≤ 405. For x = 5, 85 * 5 = 425, which is more than 405. For x = 4, 84 * 4 = 336, which is<a>less than</a>405.</p>
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<p><strong>Step 5:</strong>Subtract 336 from 405; the remainder is 69. Our quotient is now 44.</p>
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<p><strong>Step 5:</strong>Subtract 336 from 405; the remainder is 69. Our quotient is now 44.</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 6900.</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 6900.</p>
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<p><strong>Step 7:</strong>Find the new divisor, 88, by adding 4 to the quotient, making it 88x. Determine x such that 88x * x ≤ 6900. For x = 7, 887 * 7 = 6209.</p>
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<p><strong>Step 7:</strong>Find the new divisor, 88, by adding 4 to the quotient, making it 88x. Determine x such that 88x * x ≤ 6900. For x = 7, 887 * 7 = 6209.</p>
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<p><strong>Step 8:</strong>Subtracting 6209 from 6900 gives us a remainder of 691.</p>
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<p><strong>Step 8:</strong>Subtracting 6209 from 6900 gives us a remainder of 691.</p>
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<p><strong>Step 9:</strong>The quotient is now 44.7.</p>
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<p><strong>Step 9:</strong>The quotient is now 44.7.</p>
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<p><strong>Step 10:</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 10:</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 √2005 is approximately 44.78.</p>
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<p>So the square root of √2005 is approximately 44.78.</p>
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