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Original
2026-01-01
Modified
2026-02-21
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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 square root 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 square root 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 1746, we can group it as 17 and 46.</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 1746, we can group it as 17 and 46.</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 17. We can say n is '4' because 4 x 4 = 16, which is less than or equal to 17. Now the<a>quotient</a>is 4, and after subtracting 16 from 17, the<a>remainder</a>is 1.</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 17. We can say n is '4' because 4 x 4 = 16, which is less than or equal to 17. Now the<a>quotient</a>is 4, and after subtracting 16 from 17, the<a>remainder</a>is 1.</p>
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<p><strong>Step 3:</strong>Now let us bring down 46, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number, 4 + 4, we get 8, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 46, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number, 4 + 4, we get 8, which will be our new divisor.</p>
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<p><strong>Step 4:</strong>The new divisor will be the<a>sum</a>of the dividend and quotient. Now we get 8n 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<a>sum</a>of the dividend and quotient. Now we get 8n 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 8n x n ≤ 146. Let us consider n as 1; now 81 x 1 = 81.</p>
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<p><strong>Step 5:</strong>The next step is finding 8n x n ≤ 146. Let us consider n as 1; now 81 x 1 = 81.</p>
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<p><strong>Step 6:</strong>Subtract 146 from 81; the difference is 65, and the quotient is 41.</p>
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<p><strong>Step 6:</strong>Subtract 146 from 81; the difference is 65, and the quotient is 41.</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 6500.</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 6500.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor, which is 834 because 834 x 7 = 5838.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor, which is 834 because 834 x 7 = 5838.</p>
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<p><strong>Step 9:</strong>Subtracting 5838 from 6500, we get the result 662.</p>
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<p><strong>Step 9:</strong>Subtracting 5838 from 6500, we get the result 662.</p>
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<p><strong>Step 10:</strong>Now the quotient is approximately 41.7.</p>
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<p><strong>Step 10:</strong>Now the quotient is approximately 41.7.</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 value, 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 is no decimal value, continue till the remainder is zero.</p>
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<p>So the square root of √1746 is approximately 41.78.</p>
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<p>So the square root of √1746 is approximately 41.78.</p>
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