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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, we need to group the numbers from right to left. In the case of 2344, we need to group it as 23 and 44.</p>
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<p><strong>Step 1:</strong>To begin, we need to group the numbers from right to left. In the case of 2344, we need to group it as 23 and 44.</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 23. We can say n is 4 because 4 x 4 = 16, which is less than 23. The<a>quotient</a>is 4, and after subtracting 16 from 23, 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<a>less than</a>or equal to 23. We can say n is 4 because 4 x 4 = 16, which is less than 23. The<a>quotient</a>is 4, and after subtracting 16 from 23, the<a>remainder</a>is 7.</p>
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<p><strong>Step 3:</strong>Bring down 44 to form the new<a>dividend</a>, which is 744. Add the old<a>divisor</a>(4) to itself (4 + 4 = 8) to form the new divisor.</p>
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<p><strong>Step 3:</strong>Bring down 44 to form the new<a>dividend</a>, which is 744. Add the old<a>divisor</a>(4) to itself (4 + 4 = 8) to form the new divisor.</p>
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<p><strong>Step 4:</strong>Find n such that 8n x n ≤ 744. Let n be 9, then 89 x 9 = 801, which is greater than 744, so we try n = 8, 88 x 8 = 704, which fits.</p>
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<p><strong>Step 4:</strong>Find n such that 8n x n ≤ 744. Let n be 9, then 89 x 9 = 801, which is greater than 744, so we try n = 8, 88 x 8 = 704, which fits.</p>
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<p><strong>Step 5:</strong>Subtract 704 from 744, leaving a remainder of 40. The quotient is now 48.</p>
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<p><strong>Step 5:</strong>Subtract 704 from 744, leaving a remainder of 40. The quotient is now 48.</p>
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<p><strong>Step 6:</strong>Since the remainder is less than the divisor, and we need more precision, add a decimal point and bring down 00, making it 4000.</p>
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<p><strong>Step 6:</strong>Since the remainder is less than the divisor, and we need more precision, add a decimal point and bring down 00, making it 4000.</p>
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<p><strong>Step 7:</strong>Find the new divisor by doubling the current quotient (48) to get 96. Find n such that 96n x n ≤ 4000. Try n = 4, then 964 x 4 = 3856.</p>
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<p><strong>Step 7:</strong>Find the new divisor by doubling the current quotient (48) to get 96. Find n such that 96n x n ≤ 4000. Try n = 4, then 964 x 4 = 3856.</p>
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<p><strong>Step 8:</strong>Subtract 3856 from 4000, leaving a remainder of 144. The quotient is 48.4.</p>
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<p><strong>Step 8:</strong>Subtract 3856 from 4000, leaving a remainder of 144. The quotient is 48.4.</p>
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<p><strong>Step 9:</strong>Continue these steps until the desired precision is reached.</p>
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<p><strong>Step 9:</strong>Continue these steps until the desired precision is reached.</p>
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<p>The approximation of √2344 is 48.42.</p>
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<p>The approximation of √2344 is 48.42.</p>
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