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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 1412, we need to group it as 12 and 14.</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 1412, we need to group it as 12 and 14.</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 14. We can say n as ‘3’ because 3 × 3 = 9 is lesser than 14. Now the<a>quotient</a>is 3. After subtracting 9 from 14, the<a>remainder</a>is 5.</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 14. We can say n as ‘3’ because 3 × 3 = 9 is lesser than 14. Now the<a>quotient</a>is 3. After subtracting 9 from 14, the<a>remainder</a>is 5.</p>
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<p><strong>Step 3:</strong>Now, let us bring down 12 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 12 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, 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 6n 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 6n × n ≤ 512. Let us consider n as 8. Now, 68 × 8 = 544</p>
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<p><strong>Step 5:</strong>The next step is finding 6n × n ≤ 512. Let us consider n as 8. Now, 68 × 8 = 544</p>
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<p><strong>Step 6:</strong>Since 544 is greater than 512, we consider n as 7. Therefore, 67 × 7 = 469</p>
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<p><strong>Step 6:</strong>Since 544 is greater than 512, we consider n as 7. Therefore, 67 × 7 = 469</p>
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<p><strong>Step 7:</strong>Subtract 469 from 512; the difference is 43. The quotient is 37.</p>
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<p><strong>Step 7:</strong>Subtract 469 from 512; the difference is 43. The quotient is 37.</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 4300.</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 4300.</p>
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<p><strong>Step 9:</strong>Now, we need to find the new divisor, which is 754 because 754 × 4 = 3016</p>
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<p><strong>Step 9:</strong>Now, we need to find the new divisor, which is 754 because 754 × 4 = 3016</p>
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<p><strong>Step 10:</strong>Subtracting 3016 from 4300, we get the result 1284.</p>
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<p><strong>Step 10:</strong>Subtracting 3016 from 4300, we get the result 1284.</p>
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<p><strong>Step 11:</strong>The quotient is now 37.4. Step 12: 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>The quotient is now 37.4. Step 12: 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 √1412 is approximately 37.558.</p>
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<p>So, the square root of √1412 is approximately 37.558.</p>
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