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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 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 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 74, we need to group it as 74.</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 74, we need to group it as 74.</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 7. We can say n is ‘2’ because 2 x 2 = 4, which is less than 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<a>less than</a>or equal to 7. We can say n is ‘2’ because 2 x 2 = 4, which is less than 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>Bring down 4, making the new<a>dividend</a>34. Double the<a>divisor</a>, 2, to get 4.</p>
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<p><strong>Step 3:</strong>Bring down 4, making the new<a>dividend</a>34. Double the<a>divisor</a>, 2, to get 4.</p>
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<p><strong>Step 4:</strong>The next step is finding 4n × n ≤ 34. Let us consider n as 8; now 48 x 8 = 384, which is more than 34, so we try n as 7, and 47 x 7 = 329, which works.</p>
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<p><strong>Step 4:</strong>The next step is finding 4n × n ≤ 34. Let us consider n as 8; now 48 x 8 = 384, which is more than 34, so we try n as 7, and 47 x 7 = 329, which works.</p>
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<p><strong>Step 5:</strong>Subtract 329 from 340, the difference is 11, and the quotient is 8.6</p>
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<p><strong>Step 5:</strong>Subtract 329 from 340, the difference is 11, and the quotient is 8.6</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. Adding the decimal point allows us to add two zeros to the remainder. Now the new dividend is 1100.</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. Adding the decimal point allows us to add two zeros to the remainder. Now the new dividend is 1100.</p>
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<p><strong>Step 7:</strong>Find the new divisor, which is 86, because 860 x 1 = 860</p>
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<p><strong>Step 7:</strong>Find the new divisor, which is 86, because 860 x 1 = 860</p>
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<p>Continue these steps until you get the desired decimal places. So the square root of √74 ≈ 8.602</p>
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<p>Continue these steps until you get the desired decimal places. So the square root of √74 ≈ 8.602</p>
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