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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 397, we can use 3 | 97.</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 397, we can use 3 | 97.</p>
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<p><strong>Step 2:</strong>Now, we need to find a number whose square is<a>less than</a>or equal to 3. The number is 1 because 1 × 1 = 1. Now the<a>quotient</a>is 1, and after subtracting 1 from 3, the<a>remainder</a>is 2.</p>
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<p><strong>Step 2:</strong>Now, we need to find a number whose square is<a>less than</a>or equal to 3. The number is 1 because 1 × 1 = 1. Now the<a>quotient</a>is 1, and after subtracting 1 from 3, the<a>remainder</a>is 2.</p>
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<p><strong>Step 3:</strong>Bring down 97, making the new<a>dividend</a>297. Double the current quotient and add a digit to form a new<a>divisor</a>. The current quotient is 1, so 2 × 1 = 2.</p>
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<p><strong>Step 3:</strong>Bring down 97, making the new<a>dividend</a>297. Double the current quotient and add a digit to form a new<a>divisor</a>. The current quotient is 1, so 2 × 1 = 2.</p>
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<p><strong>Step 4:</strong>Now find a digit, n, such that 2n × n is less than or equal to 297. Let's consider n as 9, so 29 × 9 = 261.</p>
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<p><strong>Step 4:</strong>Now find a digit, n, such that 2n × n is less than or equal to 297. Let's consider n as 9, so 29 × 9 = 261.</p>
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<p><strong>Step 5:</strong>Subtract 261 from 297, which leaves 36. The quotient is now 19.</p>
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<p><strong>Step 5:</strong>Subtract 261 from 297, which leaves 36. The quotient is now 19.</p>
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<p><strong>Step 6:</strong>Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to continue with the process.</p>
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<p><strong>Step 6:</strong>Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to continue with the process.</p>
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<p><strong>Step 7:</strong>Add two zeroes to the dividend, making it 3600.</p>
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<p><strong>Step 7:</strong>Add two zeroes to the dividend, making it 3600.</p>
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<p><strong>Step 8:</strong>Now find a new divisor. 2 × 19 = 38, and find n such that 38n × n ≤ 3600. Let's consider n as 9, so 389 × 9 = 3501.</p>
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<p><strong>Step 8:</strong>Now find a new divisor. 2 × 19 = 38, and find n such that 38n × n ≤ 3600. Let's consider n as 9, so 389 × 9 = 3501.</p>
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<p><strong>Step 9:</strong>Subtract 3501 from 3600, which leaves 99.</p>
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<p><strong>Step 9:</strong>Subtract 3501 from 3600, which leaves 99.</p>
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<p><strong>Step 10:</strong>Now the quotient is 19.9.</p>
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<p><strong>Step 10:</strong>Now the quotient is 19.9.</p>
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<p><strong>Step 11:</strong>Continue doing these steps until we reach the desired decimal precision.</p>
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<p><strong>Step 11:</strong>Continue doing these steps until we reach the desired decimal precision.</p>
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<p>So the square root of √397 is approximately 19.933.</p>
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<p>So the square root of √397 is approximately 19.933.</p>
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