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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 3225, we need to group it as 32 and 25.</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 3225, we need to group it as 32 and 25.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is closest to 32. We can say n as ‘5’ because 5 x 5 = 25 is lesser than 32. Now the<a>quotient</a>is 5 and after subtracting 25 from 32, the<a>remainder</a>is 7.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is closest to 32. We can say n as ‘5’ because 5 x 5 = 25 is lesser than 32. Now the<a>quotient</a>is 5 and after subtracting 25 from 32, the<a>remainder</a>is 7.</p>
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<p><strong>Step 3:</strong>Now let us bring down 25 which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 5 + 5 to get 10, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 25 which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 5 + 5 to get 10, which will be our new divisor.</p>
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<p><strong>Step 4:</strong>The new divisor will be 10n. We need to find the value of n such that 10n x n ≤ 725. Let us consider n as 7, now 107 x 7 = 749, which is more than 725, so n should be<a>less than</a>7.</p>
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<p><strong>Step 4:</strong>The new divisor will be 10n. We need to find the value of n such that 10n x n ≤ 725. Let us consider n as 7, now 107 x 7 = 749, which is more than 725, so n should be<a>less than</a>7.</p>
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<p><strong>Step 5</strong>: If n = 6, then 106 x 6 = 636, which fits. Subtracting gives a remainder of 89.</p>
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<p><strong>Step 5</strong>: If n = 6, then 106 x 6 = 636, which fits. Subtracting gives a remainder of 89.</p>
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<p><strong>Step 6:</strong>Since the dividend is less than the divisor, we need to add a decimal point and add two zeroes to the dividend. Now the new dividend is 8900.</p>
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<p><strong>Step 6:</strong>Since the dividend is less than the divisor, we need to add a decimal point and add two zeroes to the dividend. Now the new dividend is 8900.</p>
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<p><strong>Step 7:</strong>Now we need to find the new divisor. Extend the divisor to 1066 and find n such that 1066n x n is close to 8900. Let n = 8, then 10668 x 8 = 85344, which is an overestimate, thus n should be less than 8.</p>
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<p><strong>Step 7:</strong>Now we need to find the new divisor. Extend the divisor to 1066 and find n such that 1066n x n is close to 8900. Let n = 8, then 10668 x 8 = 85344, which is an overestimate, thus n should be less than 8.</p>
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<p><strong>Step 8:</strong>Try n = 7, then 10667 x 7 = 74669, which fits. Subtracting gives a remainder of 1431.</p>
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<p><strong>Step 8:</strong>Try n = 7, then 10667 x 7 = 74669, which fits. Subtracting gives a remainder of 1431.</p>
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<p><strong>Step 9:</strong>Continue doing these steps until we get two numbers after the decimal point. For example, the result will approximate to 56.77. So the square root of √3225 is approximately 56.77.</p>
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<p><strong>Step 9:</strong>Continue doing these steps until we get two numbers after the decimal point. For example, the result will approximate to 56.77. So the square root of √3225 is approximately 56.77.</p>
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