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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 square root 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 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 1108, we need to group it as 08 and 11.</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 1108, we need to group it as 08 and 11.</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 11. We can say n is ‘3’ because 3 x 3 = 9 is less than 11. Now the<a>quotient</a>is 3; after subtracting 9 from 11, the<a>remainder</a>is 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 11. We can say n is ‘3’ because 3 x 3 = 9 is less than 11. Now the<a>quotient</a>is 3; after subtracting 9 from 11, the<a>remainder</a>is 2.</p>
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<p><strong>Step 3:</strong>Now let us bring down 08, making the new<a>dividend</a>208. Add the old<a>divisor</a>with the same number, 3 + 3, to get 6, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 08, making the new<a>dividend</a>208. Add the old<a>divisor</a>with the same number, 3 + 3, to get 6, which will be our new divisor.</p>
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<p><strong>Step 4:</strong>The new divisor will be in the form of 6n. We need to find the value of n where 6n x n ≤ 208. Let us consider n as 3, now 63 x 3 = 189.</p>
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<p><strong>Step 4:</strong>The new divisor will be in the form of 6n. We need to find the value of n where 6n x n ≤ 208. Let us consider n as 3, now 63 x 3 = 189.</p>
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<p><strong>Step 5:</strong>Subtract 189 from 208. The difference is 19, and the quotient becomes 33.</p>
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<p><strong>Step 5:</strong>Subtract 189 from 208. The difference is 19, and the quotient becomes 33.</p>
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<p><strong>Step 6:</strong>Since the dividend is less than the divisor, we need to add a<a>decimal</a>point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 1900.</p>
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<p><strong>Step 6:</strong>Since the dividend is less than the divisor, we need to add a<a>decimal</a>point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 1900.</p>
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<p><strong>Step 7:</strong>Now we need to find the new divisor. Trying with 33, we find 666 x 3 = 1998 is too large, so we reduce it.</p>
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<p><strong>Step 7:</strong>Now we need to find the new divisor. Trying with 33, we find 666 x 3 = 1998 is too large, so we reduce it.</p>
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<p><strong>Step 8:</strong>Using 32 with 665, we find 665 x 2 = 1330.</p>
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<p><strong>Step 8:</strong>Using 32 with 665, we find 665 x 2 = 1330.</p>
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<p><strong>Step 9:</strong>Subtracting 1330 from 1900, we get the result 570.</p>
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<p><strong>Step 9:</strong>Subtracting 1330 from 1900, we get the result 570.</p>
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<p><strong>Step 10:</strong>Now the quotient is 33.2.</p>
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<p><strong>Step 10:</strong>Now the quotient is 33.2.</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 is no decimal value, 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 is no decimal value, continue until the remainder is zero.</p>
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<p>So the square root of √1108 ≈ 33.28.</p>
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<p>So the square root of √1108 ≈ 33.28.</p>
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