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Original
2026-01-01
Modified
2026-02-28
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<p>The long<a>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 long<a>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 6121, we need to group it as 61 and 21.</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 6121, we need to group it as 61 and 21.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is close to 61. We can say n is ‘7’ because 7 × 7 = 49 is lesser than 61. Now the<a>quotient</a>is 7, and after subtracting 49 from 61, the<a>remainder</a>is 12.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is close to 61. We can say n is ‘7’ because 7 × 7 = 49 is lesser than 61. Now the<a>quotient</a>is 7, and after subtracting 49 from 61, the<a>remainder</a>is 12.</p>
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<p><strong>Step 3:</strong>Now let us bring down 21, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number, 7 + 7, to get 14, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 21, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number, 7 + 7, to get 14, 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 14n 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 14n 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 14n × n ≤ 1221. Let us consider n as 8; now 148 × 8 = 1184.</p>
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<p><strong>Step 5:</strong>The next step is finding 14n × n ≤ 1221. Let us consider n as 8; now 148 × 8 = 1184.</p>
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<p><strong>Step 6:</strong>Subtract 1184 from 1221, the difference is 37, and the quotient is 78.</p>
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<p><strong>Step 6:</strong>Subtract 1184 from 1221, the difference is 37, and the quotient is 78.</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 3700.</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 3700.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 785 because 785 × 5 = 3925.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 785 because 785 × 5 = 3925.</p>
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<p><strong>Step 9:</strong>Subtracting 3925 from 3700 gives a negative result, so we try with n = 4, and 784 × 4 = 3136.</p>
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<p><strong>Step 9:</strong>Subtracting 3925 from 3700 gives a negative result, so we try with n = 4, and 784 × 4 = 3136.</p>
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<p><strong>Step 10:</strong>Subtracting 3136 from 3700, we get the result 564.</p>
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<p><strong>Step 10:</strong>Subtracting 3136 from 3700, we get the result 564.</p>
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<p><strong>Step 11:</strong>The quotient is 78.2. Step 12: Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal values continue till the remainder is zero.</p>
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<p><strong>Step 11:</strong>The quotient is 78.2. Step 12: Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal values continue till the remainder is zero.</p>
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<p>So the square root of √6121 is approximately 78.23.</p>
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<p>So the square root of √6121 is approximately 78.23.</p>
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