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Original
2026-01-01
Modified
2026-02-28
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<p>The long<a>division</a>method is particularly used for non-perfect square numbers. In this method, we 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 long<a>division</a>method is particularly used for non-perfect square numbers. In this method, we 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>Group the numbers from right to left. In the case of 127, group it as 27 and 1.</p>
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<p><strong>Step 1:</strong>Group the numbers from right to left. In the case of 127, group it as 27 and 1.</p>
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<p><strong>Step 2:</strong>Find n whose square is<a>less than</a>or equal to 1. Here, n is 1 because 1 × 1 is less than or equal to 1. The<a>quotient</a>is 1 and the<a>remainder</a>is 0 after subtracting 1 - 1.</p>
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<p><strong>Step 2:</strong>Find n whose square is<a>less than</a>or equal to 1. Here, n is 1 because 1 × 1 is less than or equal to 1. The<a>quotient</a>is 1 and the<a>remainder</a>is 0 after subtracting 1 - 1.</p>
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<p><strong>Step 3:</strong>Bring down 27 which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number, 1 + 1, to get 2 which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Bring down 27 which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number, 1 + 1, to get 2 which will be our new divisor.</p>
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<p><strong>Step 4:</strong>Use 2 as the new divisor and find n such that 2n × n is less than or equal to 27. Let n = 5, then 2 × 5 × 5 = 50, which is<a>greater than</a>27, so try n = 4, then 2 × 4 × 4 = 32, which is also greater. Use n = 3, then 2 × 3 × 3 = 18.</p>
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<p><strong>Step 4:</strong>Use 2 as the new divisor and find n such that 2n × n is less than or equal to 27. Let n = 5, then 2 × 5 × 5 = 50, which is<a>greater than</a>27, so try n = 4, then 2 × 4 × 4 = 32, which is also greater. Use n = 3, then 2 × 3 × 3 = 18.</p>
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<p><strong>Step 5:</strong>Subtract 27 from 18, giving a remainder of 9, with the quotient now being 13.</p>
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<p><strong>Step 5:</strong>Subtract 27 from 18, giving a remainder of 9, with the quotient now being 13.</p>
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<p><strong>Step 6:</strong>Since the dividend is less than the divisor, add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. The new dividend is 900.</p>
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<p><strong>Step 6:</strong>Since the dividend is less than the divisor, add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. The new dividend is 900.</p>
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<p><strong>Step 7:</strong>Find the new divisor, using n = 4, since 246 × 4 = 984, closer to 900.</p>
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<p><strong>Step 7:</strong>Find the new divisor, using n = 4, since 246 × 4 = 984, closer to 900.</p>
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<p><strong>Step 8:</strong>Subtract 984 from 900 to get -84, which means try n = 3, resulting in 243 × 3 = 729.</p>
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<p><strong>Step 8:</strong>Subtract 984 from 900 to get -84, which means try n = 3, resulting in 243 × 3 = 729.</p>
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<p><strong>Step 9:</strong>Subtract 729 from 900, resulting in a remainder of 171.</p>
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<p><strong>Step 9:</strong>Subtract 729 from 900, resulting in a remainder of 171.</p>
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<p><strong>Step 10:</strong>The quotient is 11.3.</p>
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<p><strong>Step 10:</strong>The quotient is 11.3.</p>
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<p><strong>Step 11:</strong>Continue these steps until you get at least two decimal places or the remainder becomes zero.</p>
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<p><strong>Step 11:</strong>Continue these steps until you get at least two decimal places or the remainder becomes zero.</p>
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<p>So, the approximation of the square root of 127 is 11.27.</p>
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<p>So, the approximation of the square root of 127 is 11.27.</p>
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