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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 square root 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 square root 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 2084, we need to group it as 84 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 2084, we need to group it as 84 and 20.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is ≤ 20. We can say n as ‘4’ because 4 x 4 = 16 ≤ 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 ≤ 20. We can say n as ‘4’ because 4 x 4 = 16 ≤ 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>Now let us bring down 84, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 4 + 4, we get 8, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 84, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 4 + 4, we 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 ≤ 484. Let us consider n as 5, now 85 x 5 = 425.</p>
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<p><strong>Step 5:</strong>The next step is finding 8n × n ≤ 484. Let us consider n as 5, now 85 x 5 = 425.</p>
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<p><strong>Step 6:</strong>Subtract 425 from 484, the difference is 59, and the quotient is 45.</p>
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<p><strong>Step 6:</strong>Subtract 425 from 484, the difference is 59, and the quotient is 45.</p>
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<p><strong>Step 7:</strong>Since the dividend is<a>less than</a>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 5900.</p>
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<p><strong>Step 7:</strong>Since the dividend is<a>less than</a>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 5900.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor, which is 457 because 457 x 7 = 3199.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor, which is 457 because 457 x 7 = 3199.</p>
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<p><strong>Step 9:</strong>Subtracting 3199 from 5900, we get the result 2701.</p>
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<p><strong>Step 9:</strong>Subtracting 3199 from 5900, we get the result 2701.</p>
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<p><strong>Step 10:</strong>Now the quotient is 45.7.</p>
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<p><strong>Step 10:</strong>Now the quotient is 45.7.</p>
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<p><strong>Step 11:</strong>Continue doing these steps until we get two numbers after the decimal point. Suppose there is no decimal value, continue till the remainder is zero.</p>
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<p><strong>Step 11:</strong>Continue doing these steps until we get two numbers after the decimal point. Suppose there is no decimal value, continue till the remainder is zero.</p>
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<p>So the square root of √2084 ≈ 45.64</p>
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<p>So the square root of √2084 ≈ 45.64</p>
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