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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. 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. 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 446, we need to group it as 4 and 46.</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 446, we need to group it as 4 and 46.</p>
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<p><strong>Step 2:</strong>Find a number n whose square is ≤ 4. We can say n is 2 because 2 x 2 is<a>less than</a>or equal to 4. Now the<a>quotient</a>is 2, and after subtracting, the<a>remainder</a>is 0.</p>
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<p><strong>Step 2:</strong>Find a number n whose square is ≤ 4. We can say n is 2 because 2 x 2 is<a>less than</a>or equal to 4. Now the<a>quotient</a>is 2, and after subtracting, the<a>remainder</a>is 0.</p>
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<p><strong>Step 3:</strong>Bring down the next group, which is 46, making it the new<a>dividend</a>. 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 the next group, which is 46, making it the new<a>dividend</a>. 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 4n. Find n such that 4n x n ≤ 46. Let us consider n as 1, then 41 x 1 = 41.</p>
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<p><strong>Step 4:</strong>The new divisor will be 4n. Find n such that 4n x n ≤ 46. Let us consider n as 1, then 41 x 1 = 41.</p>
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<p><strong>Step 5:</strong>Subtract 46 from 41, the difference is 5, and the quotient is 21.</p>
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<p><strong>Step 5:</strong>Subtract 46 from 41, the difference is 5, and the quotient is 21.</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 500.</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 500.</p>
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<p><strong>Step 7:</strong>Find the new divisor that is 423 because 421 x 1 = 421.</p>
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<p><strong>Step 7:</strong>Find the new divisor that is 423 because 421 x 1 = 421.</p>
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<p><strong>Step 8:</strong>Subtracting 421 from 500 gives 79.</p>
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<p><strong>Step 8:</strong>Subtracting 421 from 500 gives 79.</p>
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<p><strong>Step 9:</strong>Continue doing these steps until we get two numbers after the decimal point. Suppose there are no decimal values, continue till the remainder is zero.</p>
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<p><strong>Step 9:</strong>Continue doing these steps until we get two numbers after the decimal point. Suppose there are no decimal values, continue till the remainder is zero.</p>
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<p><strong>So the square root of √446 ≈ 21.12.</strong></p>
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<p><strong>So the square root of √446 ≈ 21.12.</strong></p>
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