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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 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 long<a>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 458, we need to group it as 58 and 4.</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 458, we need to group it as 58 and 4.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is 4. We can say n as ‘2’ because 2 × 2 = 4. Now the<a>quotient</a>is 2, and after subtracting 4 from 4, the<a>remainder</a>is 0.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is 4. We can say n as ‘2’ because 2 × 2 = 4. Now the<a>quotient</a>is 2, and after subtracting 4 from 4, the<a>remainder</a>is 0.</p>
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<p><strong>Step 3:</strong>Now let us bring down 58 which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 2 + 2, we get 4 which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 58 which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 2 + 2, we get 4 which will be our new divisor.</p>
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<p><strong>Step 4:</strong>We need to find the value of n such that 4n × n ≤ 58. Let us consider n as 1, now 4 × 1 × 1 = 41.</p>
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<p><strong>Step 4:</strong>We need to find the value of n such that 4n × n ≤ 58. Let us consider n as 1, now 4 × 1 × 1 = 41.</p>
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<p><strong>Step 5:</strong>Subtract 58 from 41, the difference is 17, and the quotient is 21.</p>
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<p><strong>Step 5:</strong>Subtract 58 from 41, the difference is 17, and the quotient is 21.</p>
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<p><strong>Step 6:</strong>Since the dividend is<a>less than</a>the divisor, we need to add a<a>decimal</a>point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 1700.</p>
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<p><strong>Step 6:</strong>Since the dividend is<a>less than</a>the divisor, we need to add a<a>decimal</a>point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 1700.</p>
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<p><strong>Step 7:</strong>Now we need to find the new divisor that is 428 because 428 × 3 = 1284.</p>
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<p><strong>Step 7:</strong>Now we need to find the new divisor that is 428 because 428 × 3 = 1284.</p>
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<p><strong>Step 8:</strong>Subtracting 1284 from 1700, we get the result 416.</p>
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<p><strong>Step 8:</strong>Subtracting 1284 from 1700, we get the result 416.</p>
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<p><strong>Step 9:</strong>The quotient is 21.3</p>
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<p><strong>Step 9:</strong>The quotient is 21.3</p>
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<p><strong>Step 10:</strong>Continue doing these steps until we get two numbers after the decimal point.</p>
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<p><strong>Step 10:</strong>Continue doing these steps until we get two numbers after the decimal point.</p>
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<p>So the square root of √458 is approximately 21.40.</p>
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<p>So the square root of √458 is approximately 21.40.</p>
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