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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 209, we need to group it as 09 and 2.</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 209, we need to group it as 09 and 2.</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 2. We can say n as ‘1’ because 1 × 1 is less than or equal to 2. Now the<a>quotient</a>is 1, and after subtracting 1² from 2, the<a>remainder</a>is 1.<strong></strong></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 2. We can say n as ‘1’ because 1 × 1 is less than or equal to 2. Now the<a>quotient</a>is 1, and after subtracting 1² from 2, the<a>remainder</a>is 1.<strong></strong></p>
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<p><strong>Step 3:</strong>Now, let us bring down 09, 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>Now, let us bring down 09, 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>The new divisor will be the<a>sum</a>of the dividend and quotient. Now we have 2n 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 have 2n as the new divisor; we need to find the value of n.</p>
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<p><strong>Step 5:</strong>Finding 2n × n ≤ 109, let us consider n as 4. Now 24 × 4 = 96.</p>
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<p><strong>Step 5:</strong>Finding 2n × n ≤ 109, let us consider n as 4. Now 24 × 4 = 96.</p>
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<p><strong>Step 6:</strong>Subtract 96 from 109; the difference is 13, and the quotient is 14.<strong></strong></p>
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<p><strong>Step 6:</strong>Subtract 96 from 109; the difference is 13, and the quotient is 14.<strong></strong></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 1300.</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 1300.</p>
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<p><strong>Step 8</strong>: Now we need to find the new divisor that is 289 because 289 × 4 = 1156.<strong></strong></p>
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<p><strong>Step 8</strong>: Now we need to find the new divisor that is 289 because 289 × 4 = 1156.<strong></strong></p>
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<p><strong>Step 9:</strong>Subtracting 1156 from 1300, we get the result 144. Step 10: Now the quotient is 14.4.</p>
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<p><strong>Step 9:</strong>Subtracting 1156 from 1300, we get the result 144. Step 10: Now the quotient is 14.4.</p>
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<p><strong>Step 11:</strong>Continue these steps until we get two numbers after the decimal point or until the remainder is zero.</p>
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<p><strong>Step 11:</strong>Continue these steps until we get two numbers after the decimal point or until the remainder is zero.</p>
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<p>So the square root of √209 is approximately 14.46.</p>
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<p>So the square root of √209 is approximately 14.46.</p>
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