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Original
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 numbers 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 long<a>division</a>method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square numbers 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>Begin by grouping the numbers from right to left. In the case of 725, we need to group it as 25 and 7.</p>
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<p><strong>Step 1:</strong>Begin by grouping the numbers from right to left. In the case of 725, we need to group it as 25 and 7.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is ≤ 7. We can say n as ‘2’ because 2 x 2 = 4 is<a>less than</a>7. Now the<a>quotient</a>is 2, after subtracting 4 from 7, 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 ≤ 7. We can say n as ‘2’ because 2 x 2 = 4 is<a>less than</a>7. Now the<a>quotient</a>is 2, after subtracting 4 from 7, the<a>remainder</a>is 3.</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: 2 + 2 = 4, 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: 2 + 2 = 4, 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 4n as the new divisor, 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 4n as the new divisor, we need to find the value of n.</p>
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<p><strong>Step 5:</strong>The next step is finding 4n × n ≤ 325. Let us consider n as 7, now 47 x 7 = 329.</p>
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<p><strong>Step 5:</strong>The next step is finding 4n × n ≤ 325. Let us consider n as 7, now 47 x 7 = 329.</p>
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<p><strong>Step 6:</strong>Subtract 325 from 329, but since 329 is too large, try a smaller number. Use 46 x 6 = 276. Subtract 276 from 325 and the difference is 49, and the quotient is 26.</p>
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<p><strong>Step 6:</strong>Subtract 325 from 329, but since 329 is too large, try a smaller number. Use 46 x 6 = 276. Subtract 276 from 325 and the difference is 49, and the quotient is 26.</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. Try 539 since 539 x 9 = 4851.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor. Try 539 since 539 x 9 = 4851.</p>
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<p><strong>Step 9:</strong>Subtracting 4851 from 4900 gives the result 49.</p>
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<p><strong>Step 9:</strong>Subtracting 4851 from 4900 gives the result 49.</p>
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<p><strong>Step 10:</strong>Now the quotient is 26.9.</p>
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<p><strong>Step 10:</strong>Now the quotient is 26.9.</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 √725 is approximately 26.93.</p>
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<p>So the square root of √725 is approximately 26.93.</p>
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