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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 422, we need to group it as 42 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 422, we need to group it as 42 and 2.</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. 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. 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 22, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 2 + 2, we get 4, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 22, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 2 + 2, we get 4, which will be our new divisor.</p>
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<p><strong>Step 4:</strong>The new divisor will be the sum of the dividend and quotient. Now we get 4n 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 sum of the dividend and quotient. Now we get 4n 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 4n x n ≤ 22. Let us consider n as 5, now 45 x 5 = 225, which is greater than 22. So, we consider n as 4, now 44 x 4 = 176.</p>
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<p><strong>Step 5:</strong>The next step is finding 4n x n ≤ 22. Let us consider n as 5, now 45 x 5 = 225, which is greater than 22. So, we consider n as 4, now 44 x 4 = 176.</p>
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<p><strong>Step 6:</strong>Subtract 176 from 220 (since we consider 22 as 220), the difference is 44, and the quotient is 24.</p>
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<p><strong>Step 6:</strong>Subtract 176 from 220 (since we consider 22 as 220), the difference is 44, and the quotient is 24.</p>
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<p><strong>Step 7:</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 4400.</p>
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<p><strong>Step 7:</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 4400.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 409 because 409 x 5 = 2045</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 409 because 409 x 5 = 2045</p>
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<p><strong>Step 9:</strong>Subtracting 2045 from 4400, we get the result 2355.</p>
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<p><strong>Step 9:</strong>Subtracting 2045 from 4400, we get the result 2355.</p>
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<p><strong>Step 10:</strong>Now the quotient is 20.5</p>
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<p><strong>Step 10:</strong>Now the quotient is 20.5</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><strong>So the square root of √422 is approximately 20.54.</strong></p>
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<p><strong>So the square root of √422 is approximately 20.54.</strong></p>
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