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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 11016, we need to group it as 16 and 110.</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 11016, we need to group it as 16 and 110.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is<a>less than</a>or equal to 110. We can say n as ‘10’ because 10^2 = 100 is lesser than or equal to 110. Now the<a>quotient</a>is 10 after subtracting 110 - 100, the<a>remainder</a>is 10.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is<a>less than</a>or equal to 110. We can say n as ‘10’ because 10^2 = 100 is lesser than or equal to 110. Now the<a>quotient</a>is 10 after subtracting 110 - 100, the<a>remainder</a>is 10.</p>
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<p><strong>Step 3:</strong>Now let us bring down 16, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number: 10 + 10 = 20, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 16, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number: 10 + 10 = 20, which will be our new divisor.</p>
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<p><strong>Step 4:</strong>The new divisor will be 20n. We need to find the value of n that satisfies 20n × n ≤ 1016. Let us consider n as 5; now 205 × 5 = 1025.</p>
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<p><strong>Step 4:</strong>The new divisor will be 20n. We need to find the value of n that satisfies 20n × n ≤ 1016. Let us consider n as 5; now 205 × 5 = 1025.</p>
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<p><strong><em>Step 5:</em></strong>Subtract 1016 from 1025, the difference is -9. As it went negative, we take n as 4, now 204 × 4 = 816.</p>
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<p><strong><em>Step 5:</em></strong>Subtract 1016 from 1025, the difference is -9. As it went negative, we take n as 4, now 204 × 4 = 816.</p>
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<p><strong>Step 6:</strong>Subtract 1016 from 816, the difference is 200, and the quotient becomes 104.</p>
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<p><strong>Step 6:</strong>Subtract 1016 from 816, the difference is 200, and the quotient becomes 104.</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 20000.</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 20000.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor, which is 1049, because 1049 × 9 = 9441.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor, which is 1049, because 1049 × 9 = 9441.</p>
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<p><strong>Step 9:</strong>Subtracting 9441 from 20000, we get the result 10559.</p>
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<p><strong>Step 9:</strong>Subtracting 9441 from 20000, we get the result 10559.</p>
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<p><strong>Step 10:</strong>Continue repeating these steps until we get two numbers after the decimal point or a suitable approximation.</p>
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<p><strong>Step 10:</strong>Continue repeating these steps until we get two numbers after the decimal point or a suitable approximation.</p>
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<p>So the square root of √11016 is approximately 104.941.</p>
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<p>So the square root of √11016 is approximately 104.941.</p>
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