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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 with, we need to group the numbers from right to left. In the case of 2089, we need to group it as 89 and 20.</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 2089, we need to group it as 89 and 20.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is closest to 20. We can say n as '4' because 4 × 4 = 16, which is lesser than or equal to 20. Now the<a>quotient</a>is 4, and after subtracting 16 from 20, the<a>remainder</a>is 4.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is closest to 20. We can say n as '4' because 4 × 4 = 16, which is lesser than or equal to 20. Now the<a>quotient</a>is 4, and after subtracting 16 from 20, the<a>remainder</a>is 4.</p>
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<p><strong>Step 3:</strong>Bring down 89, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number, 4 + 4, to get 8, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Bring down 89, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number, 4 + 4, to get 8, 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 8n 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 8n 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 8n × n ≤ 489. Let us consider n as 5; now 85 × 5 = 425.</p>
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<p><strong>Step 5:</strong>The next step is finding 8n × n ≤ 489. Let us consider n as 5; now 85 × 5 = 425.</p>
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<p><strong>Step 6:</strong>Subtract 425 from 489; the difference is 64, and the quotient is 45.</p>
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<p><strong>Step 6:</strong>Subtract 425 from 489; the difference is 64, and the quotient is 45.</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 zeros to the dividend. Now the new dividend is 6400.</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 zeros to the dividend. Now the new dividend is 6400.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor. Consider 45.6 as the quotient to find the next step. The divisor becomes 456, and we find the next digit. 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 8:</strong>Now we need to find the new divisor. Consider 45.6 as the quotient to find the next step. The divisor becomes 456, and we find the next digit. 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 √2089 is approximately 45.70.</p>
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<p>So the square root of √2089 is approximately 45.70.</p>
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