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Original
2026-01-01
Modified
2026-02-21
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<p>This is a method used for obtaining the square root for non-<a>perfect squares</a>, mainly. It usually involves the division of the<a>dividend</a>by the<a>divisor</a>, getting a<a>quotient</a>and a<a>remainder</a>too sometimes.</p>
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<p>This is a method used for obtaining the square root for non-<a>perfect squares</a>, mainly. It usually involves the division of the<a>dividend</a>by the<a>divisor</a>, getting a<a>quotient</a>and a<a>remainder</a>too sometimes.</p>
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<p>Follow the steps to calculate the square root of 12:</p>
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<p>Follow the steps to calculate the square root of 12:</p>
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<p><strong>Step 1 :</strong>Write the number 12, and draw a horizontal bar above the pair of digits from right to left.</p>
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<p><strong>Step 1 :</strong>Write the number 12, and draw a horizontal bar above the pair of digits from right to left.</p>
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<p><strong>Step 2 :</strong>Now, find the greatest number whose square is<a>less than</a>or equal to 12. Here, it is 3, Because 32=9 < 12.</p>
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<p><strong>Step 2 :</strong>Now, find the greatest number whose square is<a>less than</a>or equal to 12. Here, it is 3, Because 32=9 < 12.</p>
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<p><strong>Step 3 :</strong>Now divide 12 by 3, such that we get 3 as a quotient and then multiply the divisor with the quotient, we get 9.</p>
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<p><strong>Step 3 :</strong>Now divide 12 by 3, such that we get 3 as a quotient and then multiply the divisor with the quotient, we get 9.</p>
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<p><strong>Step 4:</strong>Add a<a>decimal</a>point after the quotient 3, and bring down two zeroes and place it beside the difference 3 to make it 300.</p>
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<p><strong>Step 4:</strong>Add a<a>decimal</a>point after the quotient 3, and bring down two zeroes and place it beside the difference 3 to make it 300.</p>
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<p><strong>Step 5:</strong>Add 3 to the same divisor, 3. We get 6.</p>
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<p><strong>Step 5:</strong>Add 3 to the same divisor, 3. We get 6.</p>
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<p><strong>Step 6:</strong>Now choose a number such that when placed at the end of 6, a 2-digit number will be formed. Multiply that particular number by the resultant number to get a number less than 300. Here, that number is 4. 64×4=256<300.</p>
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<p><strong>Step 6:</strong>Now choose a number such that when placed at the end of 6, a 2-digit number will be formed. Multiply that particular number by the resultant number to get a number less than 300. Here, that number is 4. 64×4=256<300.</p>
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<p><strong>Step 7:</strong>Subtract 300-256=44. Again, bring down two zeroes and make 44 as 4400. Simultaneously add the unit’s place digit of 64, i.e., 4 with 64. We get here, 68. Apply Step 5 again and again until you reach 0. </p>
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<p><strong>Step 7:</strong>Subtract 300-256=44. Again, bring down two zeroes and make 44 as 4400. Simultaneously add the unit’s place digit of 64, i.e., 4 with 64. We get here, 68. Apply Step 5 again and again until you reach 0. </p>
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<p>We will show two places of precision here, and so, we are left with the remainder, 704 (refer to the picture), after some iterations and keeping the division till here, at this point </p>
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<p>We will show two places of precision here, and so, we are left with the remainder, 704 (refer to the picture), after some iterations and keeping the division till here, at this point </p>
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<p> <strong>Step 8 :</strong>The quotient obtained is the square root. In this case, it is 3.464….</p>
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<p> <strong>Step 8 :</strong>The quotient obtained is the square root. In this case, it is 3.464….</p>
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