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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 1223, we need to group it as 23 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 1223, we need to group it as 23 and 12.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is closest to 12. We can say n as ‘3’ because 3 x 3 is lesser than or equal to 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 closest to 12. We can say n as ‘3’ because 3 x 3 is lesser than or equal to 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 23, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number, 3 + 3, and we get 6, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 23, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number, 3 + 3, and 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<a>sum</a>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<a>sum</a>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 ≤ 323; let us consider n as 5, now 65 x 5 = 325</p>
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<p><strong>Step 5:</strong>The next step is finding 6n × n ≤ 323; let us consider n as 5, now 65 x 5 = 325</p>
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<p><strong>Step 6:</strong>Since 325 is greater than 323, let us consider n as 4. Now 64 x 4 = 256</p>
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<p><strong>Step 6:</strong>Since 325 is greater than 323, let us consider n as 4. Now 64 x 4 = 256</p>
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<p><strong>Step 7:</strong>Subtract 256 from 323; the difference is 67, and the quotient is 34.</p>
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<p><strong>Step 7:</strong>Subtract 256 from 323; the difference is 67, and the quotient is 34.</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 6700.</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 6700.</p>
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<p><strong>Step 9:</strong>Now we need to find the new divisor that is 9 because 679 x 9 = 6111</p>
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<p><strong>Step 9:</strong>Now we need to find the new divisor that is 9 because 679 x 9 = 6111</p>
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<p><strong>Step 10:</strong>Subtracting 6111 from 6700, we get the result 589.</p>
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<p><strong>Step 10:</strong>Subtracting 6111 from 6700, we get the result 589.</p>
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<p><strong>Step 11:</strong>Now the quotient is 34.9 Step 12: 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>Now the quotient is 34.9 Step 12: 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 √1223 is approximately 34.96.</p>
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<p>So the square root of √1223 is approximately 34.96.</p>
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