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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 110, we need to group it as 10 and 1.</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 110, we need to group it as 10 and 1.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is ≤1. We can say n as ‘1’ because 1 × 1 is<a>less than</a>or equal to 1. Now the<a>quotient</a>is 1; after subtracting 1-1, 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 ≤1. We can say n as ‘1’ because 1 × 1 is<a>less than</a>or equal to 1. Now the<a>quotient</a>is 1; after subtracting 1-1, the<a>remainder</a>is 0.</p>
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<p><strong>Step 3:</strong>Now let us bring down 10, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number, 1 + 1; we get 2, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 10, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number, 1 + 1; we get 2, which will be our new divisor.</p>
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<p><strong>Step 4:</strong>Now we get 2n as the new divisor; we need to find the value of n.</p>
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<p><strong>Step 4:</strong>Now we get 2n 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 2n × n ≤ 10. Let us consider n as 4, now 2 × 4 × 4 = 32, which is more than 10. So, we take n as 3, then 2 × 3 × 3 = 18.</p>
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<p><strong>Step 5:</strong>The next step is finding 2n × n ≤ 10. Let us consider n as 4, now 2 × 4 × 4 = 32, which is more than 10. So, we take n as 3, then 2 × 3 × 3 = 18.</p>
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<p><strong>Step 6:</strong>Subtract 10 from 18, and the difference is -8, but since we can't have a negative remainder, review steps to ensure the closest n is chosen correctly.</p>
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<p><strong>Step 6:</strong>Subtract 10 from 18, and the difference is -8, but since we can't have a negative remainder, review steps to ensure the closest n is chosen correctly.</p>
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<p><strong>Step 7:</strong>Add a decimal point to the quotient and bring down two zeros to the remainder, now making it 1000.</p>
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<p><strong>Step 7:</strong>Add a decimal point to the quotient and bring down two zeros to the remainder, now making it 1000.</p>
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<p><strong>Step 8:</strong>The new divisor becomes 26 (2n + n = 23, add another n = 26). Choose n as 3, then 263 × 3 = 789.</p>
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<p><strong>Step 8:</strong>The new divisor becomes 26 (2n + n = 23, add another n = 26). Choose n as 3, then 263 × 3 = 789.</p>
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<p><strong>Step 9:</strong>Subtracting 789 from 1000 gives us 211.</p>
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<p><strong>Step 9:</strong>Subtracting 789 from 1000 gives us 211.</p>
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<p><strong>Step 10:</strong>Continue this process until you achieve the desired decimal precision.</p>
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<p><strong>Step 10:</strong>Continue this process until you achieve the desired decimal precision.</p>
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<p>The square root of √110 is approximately 10.4881.</p>
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<p>The square root of √110 is approximately 10.4881.</p>
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