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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 392, we need to group it as 92 and 3.</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 392, we need to group it as 92 and 3.</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 3. We can say n is ‘1’ because 1 x 1 is less than or equal to 3. Now the<a>quotient</a>is 1, after subtracting 1 from 3, the<a>remainder</a>is 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 3. We can say n is ‘1’ because 1 x 1 is less than or equal to 3. Now the<a>quotient</a>is 1, after subtracting 1 from 3, the<a>remainder</a>is 2.</p>
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<p><strong>Step 3:</strong>Now let us bring down 92, 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 92, 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, 20n, needs to be determined by finding n.</p>
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<p><strong>Step 4:</strong>The new divisor, 20n, needs to be determined by finding n.</p>
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<p><strong>Step 5:</strong>The next step is finding 20n × n ≤ 292. Let us consider n as 1, now 20 x 1 x 1 = 20.</p>
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<p><strong>Step 5:</strong>The next step is finding 20n × n ≤ 292. Let us consider n as 1, now 20 x 1 x 1 = 20.</p>
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<p><strong>Step 6:</strong>Subtract 20 from 292; the difference is 272, and the quotient is 19.</p>
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<p><strong>Step 6:</strong>Subtract 20 from 292; the difference is 272, and the quotient is 19.</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 27200.</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 27200.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor, 398, because 398 x 7 = 2786.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor, 398, because 398 x 7 = 2786.</p>
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<p><strong>Step 9:</strong>Subtracting 2786 from 27200, we get the result 442.</p>
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<p><strong>Step 9:</strong>Subtracting 2786 from 27200, we get the result 442.</p>
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<p><strong>Step 10:</strong>Now the quotient is 19.7.</p>
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<p><strong>Step 10:</strong>Now the quotient is 19.7.</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 is no decimal values, continue until 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 is no decimal values, continue until the remainder is zero.</p>
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<p>So, the square root of √392 ≈ 19.80</p>
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<p>So, the square root of √392 ≈ 19.80</p>
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