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Original
2026-01-01
Modified
2026-02-28
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<p>The long<a>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 long<a>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 393, we need to group it as 93 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 393, we need to group it as 93 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 × 1 is less than or equal to 3. Now the<a>quotient</a>is 1, and after subtracting 1, 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 × 1 is less than or equal to 3. Now the<a>quotient</a>is 1, and after subtracting 1, the<a>remainder</a>is 2.</p>
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<p><strong>Step 3:</strong>Now let us bring down 93, making the new<a>dividend</a>293. Add the old<a>divisor</a>with the same number, 1 + 1, which gives us 2 as the new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 93, making the new<a>dividend</a>293. Add the old<a>divisor</a>with the same number, 1 + 1, which gives us 2 as the 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 2n as the new divisor, and 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 2n as the new divisor, and we need to find the value of n.</p>
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<p><strong>Step 5:</strong>The next step is finding 2n × n ≤ 293. Let us consider n as 9, now 29 × 9 = 261.</p>
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<p><strong>Step 5:</strong>The next step is finding 2n × n ≤ 293. Let us consider n as 9, now 29 × 9 = 261.</p>
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<p><strong>Step 6:</strong>Subtract 261 from 293, and the difference is 32. The quotient is 19.</p>
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<p><strong>Step 6:</strong>Subtract 261 from 293, and the difference is 32. 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 3200.</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 3200.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor, which is 398, because 398 × 8 = 3184.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor, which is 398, because 398 × 8 = 3184.</p>
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<p><strong>Step 9:</strong>Subtracting 3184 from 3200, we get the result 16.</p>
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<p><strong>Step 9:</strong>Subtracting 3184 from 3200, we get the result 16.</p>
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<p><strong>Step 10:</strong>Now the quotient is 19.8.</p>
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<p><strong>Step 10:</strong>Now the quotient is 19.8.</p>
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<p><strong>Step 11:</strong>Continue doing these steps until we get two numbers after the decimal point.</p>
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<p><strong>Step 11:</strong>Continue doing these steps until we get two numbers after the decimal point.</p>
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<p>So the square root of √393 ≈ 19.82.</p>
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<p>So the square root of √393 ≈ 19.82.</p>
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