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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 square root 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 square root 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 205, we need to group it as 05 and 2.</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 205, we need to group it as 05 and 2.</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 2. We can say n as ‘1’ because 1 x 1 is lesser than or equal to 2. Now the<a>quotient</a>is 1, and after subtracting 1 from 2, 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 2. We can say n as ‘1’ because 1 x 1 is lesser than or equal to 2. Now the<a>quotient</a>is 1, and after subtracting 1 from 2, the<a>remainder</a>is 1.</p>
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<p><strong>Step 3:</strong>Now let us bring down 05, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 1 + 1 to get 2, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 05, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 1 + 1 to get 2, 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 2n 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 2n 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 2n x n ≤ 105. Let us consider n as 4, now 24 x 4 = 96.</p>
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<p><strong>Step 5:</strong>The next step is finding 2n x n ≤ 105. Let us consider n as 4, now 24 x 4 = 96.</p>
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<p><strong>Step 6:</strong>Subtract 96 from 105, the difference is 9, and the quotient is 14.</p>
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<p><strong>Step 6:</strong>Subtract 96 from 105, the difference is 9, and the quotient is 14.</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 900.</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 900.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor, which is 287 because 287 x 3 = 861.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor, which is 287 because 287 x 3 = 861.</p>
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<p><strong>Step 9:</strong>Subtracting 861 from 900, we get the result 39. Step 10: Now the quotient is 14.3.</p>
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<p><strong>Step 9:</strong>Subtracting 861 from 900, we get the result 39. Step 10: Now the quotient is 14.3.</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 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. Suppose if there are no decimal values, continue until the remainder is zero.</p>
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<p>So the square root of √205 is approximately 14.31.</p>
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<p>So the square root of √205 is approximately 14.31.</p>
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