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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 1145, we need to group it as 11 and 45.</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 1145, we need to group it as 11 and 45.</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 is 3 because 3 × 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 is 3 because 3 × 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 45, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 3 + 3, we get 6, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 45, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 3 + 3, we get 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 ≤ 245. Let us consider n as 4. Now 64 × 4 = 256 is greater than 245, so we try n as 3.</p>
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<p><strong>Step 5:</strong>The next step is finding 6n × n ≤ 245. Let us consider n as 4. Now 64 × 4 = 256 is greater than 245, so we try n as 3.</p>
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<p><strong>Step 6:</strong>With n = 3, 63 × 3 = 189. Subtract 245 from 189, and the difference is 56.</p>
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<p><strong>Step 6:</strong>With n = 3, 63 × 3 = 189. Subtract 245 from 189, and the difference is 56.</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 5600.</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 5600.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor, which is 669 because 669 × 8 = 5352.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor, which is 669 because 669 × 8 = 5352.</p>
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<p><strong>Step 9:</strong>Subtracting 5352 from 5600, we get the result 248.</p>
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<p><strong>Step 9:</strong>Subtracting 5352 from 5600, we get the result 248.</p>
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<p><strong>Step 10:</strong>Now the quotient is 33.8.</p>
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<p><strong>Step 10:</strong>Now the quotient is 33.8.</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. So the square root of √1145 is approximately 33.82.</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. So the square root of √1145 is approximately 33.82.</p>
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