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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 1065, we need to group it as 65 and 10.</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 1065, we need to group it as 65 and 10.</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 10. We can say n is ‘3’ because 3 x 3 = 9, which is lesser than or equal to 10. Now the<a>quotient</a>is 3, and after subtracting 9 from 10, the<a>remainder</a>is 1.</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 10. We can say n is ‘3’ because 3 x 3 = 9, which is lesser than or equal to 10. Now the<a>quotient</a>is 3, and after subtracting 9 from 10, the<a>remainder</a>is 1.</p>
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<p><strong>Step 3:</strong>Now let us bring down 65, 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 65, 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 x n ≤ 165. Let us consider n as 2; now 62 x 2 = 124.</p>
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<p><strong>Step 5:</strong>The next step is finding 6n x n ≤ 165. Let us consider n as 2; now 62 x 2 = 124.</p>
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<p><strong>Step 6:</strong>Subtract 165 from 124; the difference is 41, and the quotient is 32.</p>
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<p><strong>Step 6:</strong>Subtract 165 from 124; the difference is 41, and the quotient is 32.</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 4100.</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 4100.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 649 because 649 x 6 = 3894.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 649 because 649 x 6 = 3894.</p>
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<p><strong>Step 9:</strong>Subtracting 3894 from 4100, we get the result 206.</p>
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<p><strong>Step 9:</strong>Subtracting 3894 from 4100, we get the result 206.</p>
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<p><strong>Step 10:</strong>Now the quotient is 32.6.</p>
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<p><strong>Step 10:</strong>Now the quotient is 32.6.</p>
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<p><strong>Step 11:</strong>Continue doing these steps until we get two numbers after the decimal point. Suppose there is no decimal value; continue until the remainder is zero.</p>
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<p><strong>Step 11:</strong>Continue doing these steps until we get two numbers after the decimal point. Suppose there is no decimal value; continue until the remainder is zero.</p>
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<p>So the square root of √1065 is approximately 32.62.</p>
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<p>So the square root of √1065 is approximately 32.62.</p>
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