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Original
2026-01-01
Modified
2026-02-21
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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 569, we need to group it as 69 and 5.</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 569, we need to group it as 69 and 5.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is ≤ 5. We can say n is ‘2’ because 2 x 2 = 4, which is lesser than or equal to 5. Now the<a>quotient</a>is 2. After subtracting 4 from 5, the<a>remainder</a>is 1.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is ≤ 5. We can say n is ‘2’ because 2 x 2 = 4, which is lesser than or equal to 5. Now the<a>quotient</a>is 2. After subtracting 4 from 5, the<a>remainder</a>is 1.</p>
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<p><strong>Step 3:</strong>Let us bring down 69, making the new<a>dividend</a>169. Add the old<a>divisor</a>to the same number 2 + 2 = 4, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Let us bring down 69, making the new<a>dividend</a>169. Add the old<a>divisor</a>to the same number 2 + 2 = 4, which will be our new divisor.</p>
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<p><strong>Step 4:</strong>The new divisor will be 4n, where we need to find the value of n. Step 5: The next step is finding 4n × n ≤ 169. Let us consider n as 4; now, 44 x 4 = 176, which is too large. Try n as 3, 43 x 3 = 129.</p>
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<p><strong>Step 4:</strong>The new divisor will be 4n, where we need to find the value of n. Step 5: The next step is finding 4n × n ≤ 169. Let us consider n as 4; now, 44 x 4 = 176, which is too large. Try n as 3, 43 x 3 = 129.</p>
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<p><strong>Step 6:</strong>Subtract 129 from 169; the difference is 40. The quotient is 23.</p>
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<p><strong>Step 6:</strong>Subtract 129 from 169; the difference is 40. The quotient is 23.</p>
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<p><strong>Step 7:</strong>Since the dividend is<a>less than</a>the divisor, we add a decimal point, allowing us to add two zeroes to the dividend. Now the new dividend is 4000.</p>
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<p><strong>Step 7:</strong>Since the dividend is<a>less than</a>the divisor, we add a decimal point, allowing us to add two zeroes to the dividend. Now the new dividend is 4000.</p>
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<p><strong>Step 8</strong>: Find the new divisor, which is 476 because 476 x 8 = 3808. Step 9: Subtracting 3808 from 4000, we get the result 192.</p>
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<p><strong>Step 8</strong>: Find the new divisor, which is 476 because 476 x 8 = 3808. Step 9: Subtracting 3808 from 4000, we get the result 192.</p>
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<p><strong>Step 10:</strong>Now the quotient is 23.8</p>
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<p><strong>Step 10:</strong>Now the quotient is 23.8</p>
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<p><strong>Step 11:</strong>Continue this process until you get two numbers after the decimal point, unless the remainder becomes zero.</p>
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<p><strong>Step 11:</strong>Continue this process until you get two numbers after the decimal point, unless the remainder becomes zero.</p>
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<p>So the square root of √569 is approximately 23.83.</p>
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<p>So the square root of √569 is approximately 23.83.</p>
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