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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 498, we need to group it as 98 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 498, we need to group it as 98 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 as ‘2’ because 2^2 = 4, which is lesser than or equal to 4. Now the<a>quotient</a>is 2; 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 as ‘2’ because 2^2 = 4, which is lesser than or equal to 4. Now the<a>quotient</a>is 2; 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 98, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 2 + 2; we get 4, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 98, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 2 + 2; we get 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 ≤ 98. Let us consider n as 2; now 4 x 2 x 2 = 16.</p>
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<p><strong>Step 5:</strong>The next step is finding 4n × n ≤ 98. Let us consider n as 2; now 4 x 2 x 2 = 16.</p>
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<p><strong>Step 6:</strong>Subtract 98 from 16; the difference is 82, and the quotient is 22.</p>
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<p><strong>Step 6:</strong>Subtract 98 from 16; the difference is 82, and the quotient is 22.</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 8200.</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 8200.</p>
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<p><strong>Step 8</strong>: Now we need to find the new divisor. Let us consider n as 9, because 449 x 9 = 4041.</p>
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<p><strong>Step 8</strong>: Now we need to find the new divisor. Let us consider n as 9, because 449 x 9 = 4041.</p>
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<p><strong>Step 9:</strong>Subtracting 4041 from 8200, we get the result 4159.</p>
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<p><strong>Step 9:</strong>Subtracting 4041 from 8200, we get the result 4159.</p>
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<p><strong>Step 10:</strong>Now the quotient is 22.9.</p>
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<p><strong>Step 10:</strong>Now the quotient is 22.9.</p>
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<p><strong>Step 11:</strong>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 11:</strong>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 √498 ≈ 22.29.</p>
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<p>So the square root of √498 ≈ 22.29.</p>
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