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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 useful 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 long<a>division</a>method is particularly useful 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, group the numbers from right to left. For 739, group it as 39 and 7.</p>
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<p><strong>Step 1:</strong>To begin with, group the numbers from right to left. For 739, group it as 39 and 7.</p>
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<p><strong>Step 2:</strong>Now find n whose square is ≤ 7. We can say n is ‘2’ because 2 × 2 = 4, which is ≤ 7. The<a>quotient</a>is 2, and after subtracting 4 from 7, the<a>remainder</a>is 3.</p>
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<p><strong>Step 2:</strong>Now find n whose square is ≤ 7. We can say n is ‘2’ because 2 × 2 = 4, which is ≤ 7. The<a>quotient</a>is 2, and after subtracting 4 from 7, the<a>remainder</a>is 3.</p>
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<p><strong>Step 3:</strong>Bring down 39, making the new<a>dividend</a>339. Add the old<a>divisor</a>with the same number, 2 + 2 = 4, to get a new divisor.</p>
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<p><strong>Step 3:</strong>Bring down 39, making the new<a>dividend</a>339. Add the old<a>divisor</a>with the same number, 2 + 2 = 4, to get a new divisor.</p>
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<p><strong>Step 4:</strong>Now find the largest n such that 4n × n ≤ 339. Let’s consider n as 8. Now, 48 × 8 = 384, which is<a>greater than</a>339. Trying n as 7, we get 47 × 7 = 329, which is less than 339.</p>
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<p><strong>Step 4:</strong>Now find the largest n such that 4n × n ≤ 339. Let’s consider n as 8. Now, 48 × 8 = 384, which is<a>greater than</a>339. Trying n as 7, we get 47 × 7 = 329, which is less than 339.</p>
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<p><strong>Step 5:</strong>Subtract 329 from 339, the difference is 10, and the quotient is 27.</p>
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<p><strong>Step 5:</strong>Subtract 329 from 339, the difference is 10, and the quotient is 27.</p>
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<p><strong>Step 6:</strong>Since the dividend is less than the divisor, we add a decimal point and two zeroes to the dividend. The new dividend is 1000.</p>
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<p><strong>Step 6:</strong>Since the dividend is less than the divisor, we add a decimal point and two zeroes to the dividend. The new dividend is 1000.</p>
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<p><strong>Step 7:</strong>Find the new divisor. The divisor is now 274, and we try n as 3, since 2743 × 3 = 8229. Continue these steps until we achieve the desired precision.</p>
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<p><strong>Step 7:</strong>Find the new divisor. The divisor is now 274, and we try n as 3, since 2743 × 3 = 8229. Continue these steps until we achieve the desired precision.</p>
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<p>The square root of √739 is approximately 27.189.</p>
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<p>The square root of √739 is approximately 27.189.</p>
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