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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 14900, we need to group it as (1)(49)(00).</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 14900, we need to group it as (1)(49)(00).</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is 1 or less. We can say n as ‘1’ because 1 x 1 is lesser than or equal to 1. Now the<a>quotient</a>is 1, and after subtracting 1 from 1, 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 1 or less. We can say n as ‘1’ because 1 x 1 is lesser than or equal to 1. Now the<a>quotient</a>is 1, and after subtracting 1 from 1, the<a>remainder</a>is 0.</p>
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<p><strong>Step 3:</strong>Now let us bring down 49, 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 49, 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 20n. We need to find the largest digit n such that 20n x n is<a>less than</a>or equal to 49. Let us consider n as 2, now 20 x 2 x 2 = 40.</p>
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<p><strong>Step 4:</strong>The new divisor will be 20n. We need to find the largest digit n such that 20n x n is<a>less than</a>or equal to 49. Let us consider n as 2, now 20 x 2 x 2 = 40.</p>
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<p><strong>Step 5:</strong>Subtract 49 from 40; the difference is 9. We bring down the next group, which is 00, making the new dividend 900.</p>
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<p><strong>Step 5:</strong>Subtract 49 from 40; the difference is 9. We bring down the next group, which is 00, making the new dividend 900.</p>
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<p><strong>Step 6:</strong>Now, double the quotient obtained so far to get 24, and find the new tentative divisor 240 + n such that (240 + n) x n ≤ 900. We find n as 3 because 243 x 3 = 729.</p>
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<p><strong>Step 6:</strong>Now, double the quotient obtained so far to get 24, and find the new tentative divisor 240 + n such that (240 + n) x n ≤ 900. We find n as 3 because 243 x 3 = 729.</p>
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<p><strong>Step 7:</strong>Subtract 900 from 729 to get a remainder of 171.</p>
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<p><strong>Step 7:</strong>Subtract 900 from 729 to get a remainder of 171.</p>
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<p><strong>Step 8:</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 17100.</p>
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<p><strong>Step 8:</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 17100.</p>
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<p><strong>Step 9:</strong>Now we need to find the new divisor, which is 244n + n, because 2446 x 6 = 14676.</p>
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<p><strong>Step 9:</strong>Now we need to find the new divisor, which is 244n + n, because 2446 x 6 = 14676.</p>
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<p><strong>Step 10:</strong>Subtracting 14676 from 17100, we get the result 2424.</p>
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<p><strong>Step 10:</strong>Subtracting 14676 from 17100, we get the result 2424.</p>
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<p><strong>Step 11:</strong>Continue doing these steps until we get the desired level of precision after the decimal point.</p>
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<p><strong>Step 11:</strong>Continue doing these steps until we get the desired level of precision after the decimal point.</p>
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<p>So the square root of √14900 is approximately 122.0655.</p>
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<p>So the square root of √14900 is approximately 122.0655.</p>
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