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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 square root 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 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 1205, we need to group it as 05 and 12.</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 1205, we need to group it as 05 and 12.</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 12. We can say n as ‘3’ because 3 x 3 = 9 is less than 12. Now the<a>quotient</a>is 3; after subtracting 9 from 12, the<a>remainder</a>is 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 12. We can say n as ‘3’ because 3 x 3 = 9 is less than 12. Now the<a>quotient</a>is 3; after subtracting 9 from 12, the<a>remainder</a>is 3.</p>
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<p><strong>Step 3:</strong>Now let us bring down 05, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 3 + 3 to get 6, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 05, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 3 + 3 to get 6, which will be our new divisor.</p>
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<p><strong>Step 4:</strong>The new divisor will be 6n. To find the value of n, we need 6n x n ≤ 305.</p>
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<p><strong>Step 4:</strong>The new divisor will be 6n. To find the value of n, we need 6n x n ≤ 305.</p>
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<p><strong>Step 5:</strong>Consider n as 5, now 65 x 5 = 325, which is<a>greater than</a>305. So consider n as 4, now 64 x 4 = 256, which is less than 305.</p>
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<p><strong>Step 5:</strong>Consider n as 5, now 65 x 5 = 325, which is<a>greater than</a>305. So consider n as 4, now 64 x 4 = 256, which is less than 305.</p>
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<p><strong>Step 6:</strong>Subtract 256 from 305; the difference is 49, and the quotient becomes 34.</p>
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<p><strong>Step 6:</strong>Subtract 256 from 305; the difference is 49, and the quotient becomes 34.</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 4900.</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 4900.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor. Let’s try 689 x 9 = 6201, which is too large. Trying 688 x 8 = 5504, still too large. Now 687 x 7 = 4809, which fits.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor. Let’s try 689 x 9 = 6201, which is too large. Trying 688 x 8 = 5504, still too large. Now 687 x 7 = 4809, which fits.</p>
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<p><strong>Step 9:</strong>Subtracting 4809 from 4900 gives the result 91.</p>
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<p><strong>Step 9:</strong>Subtracting 4809 from 4900 gives the result 91.</p>
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<p><strong>Step 10:</strong>Now the quotient is 34.7.</p>
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<p><strong>Step 10:</strong>Now the quotient is 34.7.</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 are no decimal values, 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 are no decimal values, continue till the remainder is zero.</p>
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<p>So the square root of √1205 is approximately 34.72.</p>
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<p>So the square root of √1205 is approximately 34.72.</p>
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