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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 square root 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 square root 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 2006, we need to group it as 06 and 20.</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 2006, we need to group it as 06 and 20.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is ≤ 20. We can say n is '4' because 4 x 4 = 16, which is lesser than or equal to 20. Now the<a>quotient</a>is 4, and after subtracting 16 from 20, the<a>remainder</a>is 4.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is ≤ 20. We can say n is '4' because 4 x 4 = 16, which is lesser than or equal to 20. Now the<a>quotient</a>is 4, and after subtracting 16 from 20, the<a>remainder</a>is 4.</p>
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<p><strong>Step 3:</strong>Bring down 06 to form the new<a>dividend</a>of 406. Add the old<a>divisor</a>with the same number 4 + 4 to get 8, which will be part of our new divisor.</p>
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<p><strong>Step 3:</strong>Bring down 06 to form the new<a>dividend</a>of 406. Add the old<a>divisor</a>with the same number 4 + 4 to get 8, which will be part of our new divisor.</p>
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<p><strong>Step 4:</strong>The new divisor will be 80n. We need to find the value of n such that 80n x n ≤ 406. Let's consider n as 5, now 805 x 5 = 4025, which is<a>greater than</a>406, so consider n as 4.</p>
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<p><strong>Step 4:</strong>The new divisor will be 80n. We need to find the value of n such that 80n x n ≤ 406. Let's consider n as 5, now 805 x 5 = 4025, which is<a>greater than</a>406, so consider n as 4.</p>
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<p><strong>Step 5:</strong>The next step is finding 84 x 4 = 336.</p>
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<p><strong>Step 5:</strong>The next step is finding 84 x 4 = 336.</p>
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<p><strong>Step 6:</strong>Subtract 336 from 406; the difference is 70.</p>
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<p><strong>Step 6:</strong>Subtract 336 from 406; the difference is 70.</p>
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<p><strong>Step 7:</strong>Since the dividend is<a>less than</a>the divisor, we add a decimal point and two zeroes to the dividend. The new dividend is 7000.</p>
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<p><strong>Step 7:</strong>Since the dividend is<a>less than</a>the divisor, we add a decimal point and two zeroes to the dividend. The new dividend is 7000.</p>
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<p><strong>Step 8:</strong>Find the new divisor which is 889, because 889 x 7 = 6223.</p>
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<p><strong>Step 8:</strong>Find the new divisor which is 889, because 889 x 7 = 6223.</p>
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<p><strong>Step 9:</strong>Subtracting 6223 from 7000 gives us 777.</p>
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<p><strong>Step 9:</strong>Subtracting 6223 from 7000 gives us 777.</p>
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<p><strong>Step 10:</strong>Now the quotient is 44.7</p>
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<p><strong>Step 10:</strong>Now the quotient is 44.7</p>
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<p><strong>Step 11:</strong>Continue doing these steps until we get two numbers after the decimal point. If there is no decimal value, 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. If there is no decimal value, continue till the remainder is zero.</p>
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<p>So the square root of √2006 is approximately 44.77.</p>
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<p>So the square root of √2006 is approximately 44.77.</p>
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