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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 1121, we need to group it as 21 and 11.</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 1121, we need to group it as 21 and 11.</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 11. We can say n as '3' because 3 x 3 = 9 is less than 11. Now the<a>quotient</a>is 3, and after subtracting 9 from 11, 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 11. We can say n as '3' because 3 x 3 = 9 is less than 11. Now the<a>quotient</a>is 3, and after subtracting 9 from 11, the<a>remainder</a>is 2.</p>
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<p><strong>Step 3:</strong>Now let us bring down 21, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number: 3 + 3 = 6, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 21, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number: 3 + 3 = 6, 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 6n 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 6n 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 6n × n ≤ 221. Let's consider n as 3. Now, 63 x 3 = 189.</p>
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<p><strong>Step 5:</strong>The next step is finding 6n × n ≤ 221. Let's consider n as 3. Now, 63 x 3 = 189.</p>
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<p><strong>Step 6:</strong>Subtract 189 from 221; the difference is 32, and the quotient is 33.</p>
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<p><strong>Step 6:</strong>Subtract 189 from 221; the difference is 32, and the quotient is 33.</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 and quotient. Using approximation, we get 334 x 4 = 1336.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor and quotient. Using approximation, we get 334 x 4 = 1336.</p>
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<p><strong>Step 9:</strong>Subtracting 1336 from 3200, we get the result 1864.</p>
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<p><strong>Step 9:</strong>Subtracting 1336 from 3200, we get the result 1864.</p>
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<p><strong>Step 10:</strong>Now the quotient is 33.4.</p>
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<p><strong>Step 10:</strong>Now the quotient is 33.4.</p>
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<p><strong>Step 11:</strong>Continue doing these steps until we get two decimal places. So the approximate square root of √1121 is 33.487.</p>
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<p><strong>Step 11:</strong>Continue doing these steps until we get two decimal places. So the approximate square root of √1121 is 33.487.</p>
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