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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 465, we need to group it as 65 and 4.</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 465, we need to group it as 65 and 4.</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 4. We can say n as '2' because 2 x 2 = 4, which is less than or equal to 4. Now the<a>quotient</a>is 2, and after subtracting 4 - 4, the<a>remainder</a>is 0.</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 4. We can say n as '2' because 2 x 2 = 4, which is less than or equal to 4. Now the<a>quotient</a>is 2, and after subtracting 4 - 4, the<a>remainder</a>is 0.</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 2 + 2 = 4, 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 2 + 2 = 4, which will be our new divisor.</p>
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<p><strong>Step 4:</strong>The new divisor will be 2n, so we need to find the value of n such that 2n x n ≤ 65. Let us consider n as 1, now 41 x 1 = 41.</p>
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<p><strong>Step 4:</strong>The new divisor will be 2n, so we need to find the value of n such that 2n x n ≤ 65. Let us consider n as 1, now 41 x 1 = 41.</p>
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<p><strong>Step 5:</strong>Subtract 41 from 65; the difference is 24, and the quotient is 21.</p>
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<p><strong>Step 5:</strong>Subtract 41 from 65; the difference is 24, and the quotient is 21.</p>
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<p><strong>Step 6:</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 2400.</p>
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<p><strong>Step 6:</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 2400.</p>
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<p><strong>Step 7:</strong>Now we need to find the new divisor that is 423. Let's consider n as 5 because 425 x 5 = 2125.</p>
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<p><strong>Step 7:</strong>Now we need to find the new divisor that is 423. Let's consider n as 5 because 425 x 5 = 2125.</p>
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<p><strong>Step 8:</strong>Subtracting 2125 from 2400, we get the result 275.</p>
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<p><strong>Step 8:</strong>Subtracting 2125 from 2400, we get the result 275.</p>
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<p><strong>Step 9:</strong>Now the quotient is 21.5</p>
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<p><strong>Step 9:</strong>Now the quotient is 21.5</p>
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<p><strong>Step 10:</strong>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 10:</strong>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 √465 is approximately 21.56.</p>
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<p>So the square root of √465 is approximately 21.56.</p>
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