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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<a>square root</a>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<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 2042, we need to group it as 42 and 20.</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 2042, we need to group it as 42 and 20.</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 20. We can choose n as 4 because 4 x 4 = 16, which is less than 20. Now the<a>quotient</a>is 4, and after subtracting 16 from 20, the<a>remainder</a>is 4.</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 20. We can choose n as 4 because 4 x 4 = 16, which is less than 20. Now the<a>quotient</a>is 4, and after subtracting 16 from 20, the<a>remainder</a>is 4.</p>
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<p><strong>Step 3:</strong>Bring down 42, making the new<a>dividend</a>442.</p>
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<p><strong>Step 3:</strong>Bring down 42, making the new<a>dividend</a>442.</p>
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<p><strong>Step 4:</strong>Double the<a>divisor</a>, which was 4, to get 8. Now find a digit x such that 8x × x is less than or equal to 442. The closest value is 85, where 85 x 5 = 425.</p>
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<p><strong>Step 4:</strong>Double the<a>divisor</a>, which was 4, to get 8. Now find a digit x such that 8x × x is less than or equal to 442. The closest value is 85, where 85 x 5 = 425.</p>
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<p><strong>Step 5:</strong>Subtract 425 from 442 to get 17, and the quotient is 45.</p>
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<p><strong>Step 5:</strong>Subtract 425 from 442 to get 17, and the quotient is 45.</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 add two zeroes to the dividend, making it 1700.</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 add two zeroes to the dividend, making it 1700.</p>
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<p><strong>Step 7:</strong>Double the current quotient and add it to the current divisor to get a new divisor, which becomes 905. Find a digit, let's say 1, such that 9051 x 1 is less than or equal to 1700.</p>
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<p><strong>Step 7:</strong>Double the current quotient and add it to the current divisor to get a new divisor, which becomes 905. Find a digit, let's say 1, such that 9051 x 1 is less than or equal to 1700.</p>
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<p><strong>Step 8:</strong>Continue this process to achieve the desired decimal places.</p>
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<p><strong>Step 8:</strong>Continue this process to achieve the desired decimal places.</p>
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<p>The approximate square root of 2042 is 45.179.</p>
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<p>The approximate square root of 2042 is 45.179.</p>
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