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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 5328, we need to group it as 28 and 53.</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 5328, we need to group it as 28 and 53.</p>
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<p><strong>Step 2:</strong>Now we need to find a number whose square is closest to 53. We can say n is '7' because 7 x 7 = 49, which is<a>less than</a>53. Now the<a>quotient</a>is 7, and after subtracting 49 from 53, the<a>remainder</a>is 4.</p>
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<p><strong>Step 2:</strong>Now we need to find a number whose square is closest to 53. We can say n is '7' because 7 x 7 = 49, which is<a>less than</a>53. Now the<a>quotient</a>is 7, and after subtracting 49 from 53, the<a>remainder</a>is 4.</p>
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<p><strong>Step 3:</strong>Bring down 28, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number: 7 + 7 = 14, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Bring down 28, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number: 7 + 7 = 14, which will be our new divisor.</p>
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<p><strong>Step 4:</strong>The new divisor is 2n. Now we need to find the value of n.</p>
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<p><strong>Step 4:</strong>The new divisor is 2n. Now we need to find the value of n.</p>
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<p><strong>Step 5:</strong>The next step is finding 14n x n ≤ 428. Let's consider n as 3, now 143 x 3 = 429, which is greater than 428, so we try n = 2, then 142 x 2 = 284.</p>
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<p><strong>Step 5:</strong>The next step is finding 14n x n ≤ 428. Let's consider n as 3, now 143 x 3 = 429, which is greater than 428, so we try n = 2, then 142 x 2 = 284.</p>
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<p><strong>Step 6:</strong>Subtract 284 from 428; the difference is 144.</p>
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<p><strong>Step 6:</strong>Subtract 284 from 428; the difference is 144.</p>
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<p><strong>Step 7:</strong>Since the dividend is not zero, 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 14400.</p>
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<p><strong>Step 7:</strong>Since the dividend is not zero, 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 14400.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor, which is 1472 because 1472 x 9 = 13248.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor, which is 1472 because 1472 x 9 = 13248.</p>
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<p><strong>Step 9:</strong>Subtract 13248 from 14400; we get the result 1152.</p>
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<p><strong>Step 9:</strong>Subtract 13248 from 14400; we get the result 1152.</p>
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<p><strong>Step 10:</strong>Now the quotient is 73.9</p>
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<p><strong>Step 10:</strong>Now the quotient is 73.9</p>
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<p><strong>Step 11:</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 11:</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 √5328 is approximately 73.</p>
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<p>So the square root of √5328 is approximately 73.</p>
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