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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 313, we need to group it as 13 and 3.</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 313, we need to group it as 13 and 3.</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 3. We can say n is ‘1’ because 1 × 1 is lesser than or equal to 3. Now the<a>quotient</a>is 1, after subtracting 1 from 3 the<a>remainder</a>is 2.</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 3. We can say n is ‘1’ because 1 × 1 is lesser than or equal to 3. Now the<a>quotient</a>is 1, after subtracting 1 from 3 the<a>remainder</a>is 2.</p>
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<p><strong>Step 3:</strong>Now let us bring down 13 which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 1 + 1, we get 2 which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 13 which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 1 + 1, we get 2 which will be our new divisor.</p>
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<p><strong>Step 4:</strong>Find a digit n such that 2n × n is less than or equal to 213. The suitable n is 8, giving us 28 × 8 = 224.</p>
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<p><strong>Step 4:</strong>Find a digit n such that 2n × n is less than or equal to 213. The suitable n is 8, giving us 28 × 8 = 224.</p>
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<p><strong>Step 5:</strong>Subtract 213 from 224, the difference is -11, and the quotient is 18.</p>
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<p><strong>Step 5:</strong>Subtract 213 from 224, the difference is -11, and the quotient is 18.</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 1100.</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 1100.</p>
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<p><strong>Step 7:</strong>The new divisor becomes 36, and the divisor times the next digit should be less than or equal to 1100. Using 3, 363 × 3 = 1089.</p>
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<p><strong>Step 7:</strong>The new divisor becomes 36, and the divisor times the next digit should be less than or equal to 1100. Using 3, 363 × 3 = 1089.</p>
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<p><strong>Step 8:</strong>Subtracting 1089 from 1100, we get 11.</p>
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<p><strong>Step 8:</strong>Subtracting 1089 from 1100, we get 11.</p>
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<p><strong>Step 9:</strong>Continue this process until you have the desired decimal places in the quotient.</p>
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<p><strong>Step 9:</strong>Continue this process until you have the desired decimal places in the quotient.</p>
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<p>The square root of √313 ≈ 17.691.</p>
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<p>The square root of √313 ≈ 17.691.</p>
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