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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 545, we group it as 45 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 545, we group it as 45 and 5.</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 5. We can say n is '2' because 2 × 2 = 4, which is less than or equal to 5. Now the<a>quotient</a>is 2, and 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<a>less than</a>or equal to 5. We can say n is '2' because 2 × 2 = 4, which is less than or equal to 5. Now the<a>quotient</a>is 2, and after subtracting 4 from 5, the<a>remainder</a>is 1.</p>
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<p><strong>Step 3:</strong>Now let us bring down 45, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 2 + 2 to get 4, which will be our new divisor prefix.</p>
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<p><strong>Step 3:</strong>Now let us bring down 45, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 2 + 2 to get 4, which will be our new divisor prefix.</p>
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<p><strong>Step 4:</strong>The new divisor will be the sum of the previous quotient and the new digit. Now we get 4n as the new divisor, and we need to find the value of n such that 4n × n ≤ 145.</p>
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<p><strong>Step 4:</strong>The new divisor will be the sum of the previous quotient and the new digit. Now we get 4n as the new divisor, and we need to find the value of n such that 4n × n ≤ 145.</p>
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<p><strong>Step 5:</strong>Considering n as 3, 43 × 3 = 129.</p>
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<p><strong>Step 5:</strong>Considering n as 3, 43 × 3 = 129.</p>
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<p><strong>Step 6:</strong>Subtract 129 from 145, the difference is 16, and the quotient now is 23.</p>
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<p><strong>Step 6:</strong>Subtract 129 from 145, the difference is 16, and the quotient now is 23.</p>
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<p>Step 7: 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. The new dividend is 1600.</p>
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<p>Step 7: 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. The new dividend is 1600.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor, which is 466 because 466 × 3 = 1398.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor, which is 466 because 466 × 3 = 1398.</p>
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<p><strong>Step 9:</strong>Subtracting 1398 from 1600, we get the result 202. Step 10: Now the quotient is 23.3.</p>
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<p><strong>Step 9:</strong>Subtracting 1398 from 1600, we get the result 202. Step 10: Now the quotient is 23.3.</p>
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<p><strong>Step 11:</strong>Continue these steps until we get the desired accuracy.</p>
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<p><strong>Step 11:</strong>Continue these steps until we get the desired accuracy.</p>
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<p>So the square root of √545 is approximately 23.345.</p>
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<p>So the square root of √545 is approximately 23.345.</p>
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