0 added
0 removed
Original
2026-01-01
Modified
2026-02-28
1
<p>The<a>long division</a>method is particularly used for non-perfect square numbers. Let us now learn how to find the<a>square root</a>using the long division method, step by step.</p>
1
<p>The<a>long division</a>method is particularly used for non-perfect square numbers. Let us now learn how to find the<a>square root</a>using the long division method, step by step.</p>
2
<p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 278, we need to group it as 78 and 2.</p>
2
<p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 278, we need to group it as 78 and 2.</p>
3
<p><strong>Step 2:</strong>Now we need to find n whose square is<a>less than</a>or equal to 2. We can say n is 1 because 1 x 1 = 1 is less than 2. Now the<a>quotient</a>is 1, and after subtracting 1 from 2, the<a>remainder</a>is 1.</p>
3
<p><strong>Step 2:</strong>Now we need to find n whose square is<a>less than</a>or equal to 2. We can say n is 1 because 1 x 1 = 1 is less than 2. Now the<a>quotient</a>is 1, and after subtracting 1 from 2, the<a>remainder</a>is 1.</p>
4
<p><strong>Step 3:</strong>Bring down 78, the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 1 + 1 to get 2, which will be our new divisor.</p>
4
<p><strong>Step 3:</strong>Bring down 78, the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 1 + 1 to get 2, which will be our new divisor.</p>
5
<p><strong>Step 4:</strong>Now, considering 2n as the new divisor, we need to find the value of n.</p>
5
<p><strong>Step 4:</strong>Now, considering 2n as the new divisor, we need to find the value of n.</p>
6
<p><strong>Step 5:</strong>We need 2n x n ≤ 178. Let us consider n as 6, then 26 x 6 = 156.</p>
6
<p><strong>Step 5:</strong>We need 2n x n ≤ 178. Let us consider n as 6, then 26 x 6 = 156.</p>
7
<p><strong>Step 6:</strong>Subtract 156 from 178; the difference is 22, and the quotient is 16.</p>
7
<p><strong>Step 6:</strong>Subtract 156 from 178; the difference is 22, and the quotient is 16.</p>
8
<p><strong>Step 7:</strong>Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to extend the dividend with two zeros. Now the new dividend is 2200.</p>
8
<p><strong>Step 7:</strong>Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to extend the dividend with two zeros. Now the new dividend is 2200.</p>
9
<p><strong>Step 8:</strong>Find the new divisor, which is 333, because 333 x 6 = 1998.</p>
9
<p><strong>Step 8:</strong>Find the new divisor, which is 333, because 333 x 6 = 1998.</p>
10
<p><strong>Step 9:</strong>Subtracting 1998 from 2200, we get the result 202.</p>
10
<p><strong>Step 9:</strong>Subtracting 1998 from 2200, we get the result 202.</p>
11
<p><strong>Step 10:</strong>Now the quotient is 16.6.</p>
11
<p><strong>Step 10:</strong>Now the quotient is 16.6.</p>
12
<p><strong>Step 11:</strong>Continue doing these steps until we get two numbers after the decimal point. If there is no decimal value, continue till the remainder is zero.</p>
12
<p><strong>Step 11:</strong>Continue doing these steps until we get two numbers after the decimal point. If there is no decimal value, continue till the remainder is zero.</p>
13
<p>So the square root of √278 is approximately 16.67.</p>
13
<p>So the square root of √278 is approximately 16.67.</p>
14
14