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Original
2026-01-01
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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 308, we group it as 08 and 3.</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 308, we group it as 08 and 3.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is ≤ 3. We can say n is ‘1’ because 1 x 1 is<a>less than</a>or equal to 3. Now the<a>quotient</a>is 1; after subtracting 1 from 3, 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 ≤ 3. We can say n is ‘1’ because 1 x 1 is<a>less than</a>or equal to 3. Now the<a>quotient</a>is 1; after subtracting 1 from 3, the<a>remainder</a>is 2.</p>
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<p><strong>Step 3:</strong>Now let us bring down 08, 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 08, 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 sum of the dividend and quotient. Now we get 2n as the new divisor, and we need to find the value of n.</p>
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<p><strong>Step 4:</strong>The new divisor will be the sum of the dividend and quotient. Now we get 2n as the new divisor, and we need to find the value of n.</p>
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<p><strong>Step 5:</strong>The next step is finding 2n × n ≤ 208. Let us consider n as 9, now 29 x 9 = 261.</p>
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<p><strong>Step 5:</strong>The next step is finding 2n × n ≤ 208. Let us consider n as 9, now 29 x 9 = 261.</p>
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<p><strong>Step 6:</strong>Subtract 208 from 261 (reverse the operation to check), and the difference is negative, so we try n = 7, now 27 x 7 = 189.</p>
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<p><strong>Step 6:</strong>Subtract 208 from 261 (reverse the operation to check), and the difference is negative, so we try n = 7, now 27 x 7 = 189.</p>
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<p><strong>Step 7:</strong>Subtracting 189 from 208, the difference is 19, and the quotient is 17.</p>
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<p><strong>Step 7:</strong>Subtracting 189 from 208, the difference is 19, and the quotient is 17.</p>
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<p><strong>Step 8:</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 1900.</p>
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<p><strong>Step 8:</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 1900.</p>
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<p><strong>Step 9:</strong>Now we need to find the new divisor. We use 350 to multiply by 5 to get 1750.</p>
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<p><strong>Step 9:</strong>Now we need to find the new divisor. We use 350 to multiply by 5 to get 1750.</p>
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<p><strong>Step 10:</strong>Subtracting 1750 from 1900, we get the result 150.</p>
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<p><strong>Step 10:</strong>Subtracting 1750 from 1900, we get the result 150.</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 √308 is approximately 17.55.</p>
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<p>So the square root of √308 is approximately 17.55.</p>
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