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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 5746, we need to group it as 46 and 57.</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 5746, we need to group it as 46 and 57.</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 57. We can say n as ‘7’ because 7 × 7 = 49 is less than 57. Now the<a>quotient</a>is 7, and after subtracting 49 from 57, the<a>remainder</a>is 8.</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 57. We can say n as ‘7’ because 7 × 7 = 49 is less than 57. Now the<a>quotient</a>is 7, and after subtracting 49 from 57, the<a>remainder</a>is 8.</p>
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<p><strong>Step 3:</strong>Now let us bring down 46, making the new<a>dividend</a>846. Add the old<a>divisor</a>with the same number, 7 + 7, which gives us 14 as the new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 46, making the new<a>dividend</a>846. Add the old<a>divisor</a>with the same number, 7 + 7, which gives us 14 as the new divisor.</p>
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<p><strong>Step 4:</strong>The next step is to find 2n × n ≤ 846. Let us consider n as 5, making 145 × 5 = 725.</p>
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<p><strong>Step 4:</strong>The next step is to find 2n × n ≤ 846. Let us consider n as 5, making 145 × 5 = 725.</p>
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<p><strong>Step 5:</strong>Subtract 725 from 846; the difference is 121.</p>
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<p><strong>Step 5:</strong>Subtract 725 from 846; the difference is 121.</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. Now the new dividend is 12100.</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. Now the new dividend is 12100.</p>
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<p><strong>Step 7:</strong>Now we need to find the new divisor that is 150, because 150 × 8 = 1200.</p>
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<p><strong>Step 7:</strong>Now we need to find the new divisor that is 150, because 150 × 8 = 1200.</p>
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<p><strong>Step 8:</strong>Subtracting 1200 from 12100, we get the result 100.</p>
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<p><strong>Step 8:</strong>Subtracting 1200 from 12100, we get the result 100.</p>
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<p><strong>Step 9:</strong>Continue doing these steps until we get two numbers after the decimal point. Suppose there are no decimal values, continue till the remainder is zero.</p>
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<p><strong>Step 9:</strong>Continue doing these steps until we get two numbers after the decimal point. Suppose there are no decimal values, continue till the remainder is zero.</p>
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<p>So the square root of √5746 ≈ 75.80.</p>
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<p>So the square root of √5746 ≈ 75.80.</p>
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