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Original
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 282, we need to group it as 82 and 2.</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 282, we need to group it as 82 and 2.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is 2. We can say n as ‘1’ because 1 x 1 is lesser than or equal to 2. Now the<a>quotient</a>is 1, and after subtracting 1 from 2, 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 2. We can say n as ‘1’ because 1 x 1 is lesser than or equal to 2. Now the<a>quotient</a>is 1, and after subtracting 1 from 2, the<a>remainder</a>is 1.</p>
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<p><strong>Step 3:</strong>Now let us bring down 82, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 1 + 1, we get 2, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 82, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 1 + 1, we get 2, 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 2n 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 2n 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 2n x n ≤ 182. Let us consider n as 8, now 28 x 8 = 224.</p>
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<p><strong>Step 5:</strong>The next step is finding 2n x n ≤ 182. Let us consider n as 8, now 28 x 8 = 224.</p>
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<p><strong>Step 6:</strong>Subtract 224 from 182, the difference is negative, so n must be less than 8. Try n = 7, now 27 x 7 = 189 which is still larger than 182.</p>
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<p><strong>Step 6:</strong>Subtract 224 from 182, the difference is negative, so n must be less than 8. Try n = 7, now 27 x 7 = 189 which is still larger than 182.</p>
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<p><strong>Step 7:</strong>Try n = 6, now 26 x 6 = 156 which is less than 182.</p>
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<p><strong>Step 7:</strong>Try n = 6, now 26 x 6 = 156 which is less than 182.</p>
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<p><strong>Step 8:</strong>Subtract 156 from 182, the difference is 26, and the quotient is 16.</p>
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<p><strong>Step 8:</strong>Subtract 156 from 182, the difference is 26, and the quotient is 16.</p>
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<p><strong>Step 9:</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 2600.</p>
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<p><strong>Step 9:</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 2600.</p>
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<p><strong>Step 10:</strong>Now we need to find the new divisor. Add the previous quotient, 16, to the divisor, 26, forming 272. Consider n as 9, 2729 x 9 = 24561, which is larger than 26000.</p>
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<p><strong>Step 10:</strong>Now we need to find the new divisor. Add the previous quotient, 16, to the divisor, 26, forming 272. Consider n as 9, 2729 x 9 = 24561, which is larger than 26000.</p>
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<p><strong>Step 11:</strong>Try n = 8, now 2728 x 8 = 21824, which is less than 26000.</p>
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<p><strong>Step 11:</strong>Try n = 8, now 2728 x 8 = 21824, which is less than 26000.</p>
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<p><strong>Step 12:</strong>Subtract 21824 from 26000, the remainder is 4176, and the new quotient is 16.8.</p>
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<p><strong>Step 12:</strong>Subtract 21824 from 26000, the remainder is 4176, and the new quotient is 16.8.</p>
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<p><strong>Step 13:</strong>Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal value continue till the remainder is zero.</p>
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<p><strong>Step 13:</strong>Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal value continue till the remainder is zero.</p>
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<p>So the square root of √282 is approximately 16.79.</p>
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<p>So the square root of √282 is approximately 16.79.</p>
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