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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<a>square root</a>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<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 1268, we need to group it as 68 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 1268, we need to group it as 68 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 is ‘3’ because 3 × 3 = 9, which is less than 12. Now the<a>quotient</a>is 3, and after subtracting 9 from 12, 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 is ‘3’ because 3 × 3 = 9, which is less than 12. Now the<a>quotient</a>is 3, and after subtracting 9 from 12, the<a>remainder</a>is 3.</p>
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<p><strong>Step 3:</strong>Now let us bring down 68, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 3 + 3, we get 6, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 68, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 3 + 3, we get 6, 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 6n 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 sum of the dividend and quotient. Now we get 6n 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 6n × n ≤ 368. Let us consider n as 6; now 6 × 6 = 36, and 66 × 6 = 396, which is greater than 368, so we try n as 5.</p>
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<p><strong>Step 5:</strong>The next step is finding 6n × n ≤ 368. Let us consider n as 6; now 6 × 6 = 36, and 66 × 6 = 396, which is greater than 368, so we try n as 5.</p>
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<p><strong>Step 6:</strong>Subtracting 330 (65 × 5) from 368, the difference is 38, and the quotient is 35.</p>
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<p><strong>Step 6:</strong>Subtracting 330 (65 × 5) from 368, the difference is 38, and the quotient is 35.</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 3800.</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 3800.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor, which is 705, because 705 × 5 = 3525.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor, which is 705, because 705 × 5 = 3525.</p>
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<p><strong>Step 9:</strong>Subtracting 3525 from 3800, we get the result 275.</p>
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<p><strong>Step 9:</strong>Subtracting 3525 from 3800, we get the result 275.</p>
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<p><strong>Step 10:</strong>Now the quotient is 35.5.</p>
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<p><strong>Step 10:</strong>Now the quotient is 35.5.</p>
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<p><strong>Step 11:</strong>Continue doing these steps until we get two numbers after the decimal point.</p>
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<p><strong>Step 11:</strong>Continue doing these steps until we get two numbers after the decimal point.</p>
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<p>So the square root of √1268 ≈ 35.60.</p>
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<p>So the square root of √1268 ≈ 35.60.</p>
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