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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 1216, we need to group it as 16 and 12.</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 1216, we need to group it as 16 and 12.</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 12. We can say n as ‘3’ because 3 x 3 = 9, and 9 is less than 12. Now the<a>quotient</a>is 3 after subtracting 12 - 9, the<a>remainder</a>is 3.</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 12. We can say n as ‘3’ because 3 x 3 = 9, and 9 is less than 12. Now the<a>quotient</a>is 3 after subtracting 12 - 9, the<a>remainder</a>is 3.</p>
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<p><strong>Step 3:</strong>Now let us bring down 16, making the new<a>dividend</a>316. 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 16, making the new<a>dividend</a>316. 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 60n, where n is the next digit in the quotient. We need to find the value of n such that 60n x n ≤ 316.</p>
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<p><strong>Step 4:</strong>The new divisor will be 60n, where n is the next digit in the quotient. We need to find the value of n such that 60n x n ≤ 316.</p>
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<p><strong>Step 5:</strong>The next step is finding the largest n such that 60n x n ≤ 316. Let us consider n as 5; now, 60 x 5 x 5 = 1500, which is too large. Trying n = 4 gives 60 x 4 x 4 = 960, still too large. Trying n = 3 gives 60 x 3 x 3 = 540, which is still too large. Trying n = 2 gives 60 x 2 x 2 = 240, which is less than 316.</p>
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<p><strong>Step 5:</strong>The next step is finding the largest n such that 60n x n ≤ 316. Let us consider n as 5; now, 60 x 5 x 5 = 1500, which is too large. Trying n = 4 gives 60 x 4 x 4 = 960, still too large. Trying n = 3 gives 60 x 3 x 3 = 540, which is still too large. Trying n = 2 gives 60 x 2 x 2 = 240, which is less than 316.</p>
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<p><strong>Step 6:</strong>Subtract 240 from 316; the difference is 76, and the quotient becomes 32.</p>
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<p><strong>Step 6:</strong>Subtract 240 from 316; the difference is 76, and the quotient becomes 32.</p>
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<p><strong>Step 7:</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, making it 7600.</p>
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<p><strong>Step 7:</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, making it 7600.</p>
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<p><strong>Step 8:</strong>Now, find the new divisor, which is 640 because 640 x 1 = 640, and 640 is less than 760.</p>
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<p><strong>Step 8:</strong>Now, find the new divisor, which is 640 because 640 x 1 = 640, and 640 is less than 760.</p>
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<p><strong>Step 9:</strong>Subtracting 640 from 760 gives a result of 120.</p>
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<p><strong>Step 9:</strong>Subtracting 640 from 760 gives a result of 120.</p>
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<p><strong>Step 10:</strong>Now the quotient is 34.8.</p>
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<p><strong>Step 10:</strong>Now the quotient is 34.8.</p>
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<p><strong>Step 11:</strong>Continue doing these steps until we get sufficient decimal places.</p>
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<p><strong>Step 11:</strong>Continue doing these steps until we get sufficient decimal places.</p>
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<p>So the square root of √1216 is approximately 34.865.</p>
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<p>So the square root of √1216 is approximately 34.865.</p>
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