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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. 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. 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 421, we can group it as 21 and 4.</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 421, we can group it as 21 and 4.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is ≤ 4. We can say n is 2 because 2 × 2 = 4. Now the<a>quotient</a>is 2, and after subtracting 4 from 4, the<a>remainder</a>is 0.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is ≤ 4. We can say n is 2 because 2 × 2 = 4. Now the<a>quotient</a>is 2, and after subtracting 4 from 4, the<a>remainder</a>is 0.</p>
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<p><strong>Step 3:</strong>Now let us bring down 21, 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 21, 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<a>sum</a>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<a>sum</a>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 ≤ 21. Let us consider n as 5, now 4 × 5 = 20, and 20 × 5 = 100, which is too large. Adjust n accordingly.</p>
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<p><strong>Step 5:</strong>The next step is finding 4n × n ≤ 21. Let us consider n as 5, now 4 × 5 = 20, and 20 × 5 = 100, which is too large. Adjust n accordingly.</p>
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<p><strong>Step 6:</strong>Subtract 21 from 20, the difference is 1, and the quotient is 20.</p>
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<p><strong>Step 6:</strong>Subtract 21 from 20, the difference is 1, and the quotient is 20.</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 100.</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 100.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is approximately 204, as 204 × 5 = 1020.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is approximately 204, as 204 × 5 = 1020.</p>
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<p><strong>Step 9:</strong>Adjust and continue the process until sufficient decimal accuracy is achieved.</p>
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<p><strong>Step 9:</strong>Adjust and continue the process until sufficient decimal accuracy is achieved.</p>
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<p><strong>Step 10:</strong>The quotient becomes approximately 20.518.</p>
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<p><strong>Step 10:</strong>The quotient becomes approximately 20.518.</p>
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