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. 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>
1
<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>
2
<p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 462, we need to group it as 62 and 4.</p>
2
<p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 462, we need to group it as 62 and 4.</p>
3
<p><strong>Step 2:</strong>Now we need to find n whose square is 4. We can say n as ‘2’ because 2 x 2 is equal to 4. Now the<a>quotient</a>is 2, and after subtracting 4 - 4, the<a>remainder</a>is 0.</p>
3
<p><strong>Step 2:</strong>Now we need to find n whose square is 4. We can say n as ‘2’ because 2 x 2 is equal to 4. Now the<a>quotient</a>is 2, and after subtracting 4 - 4, the<a>remainder</a>is 0.</p>
4
<p><strong>Step 3:</strong>Now let us bring down 62, 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>
4
<p><strong>Step 3:</strong>Now let us bring down 62, 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>
5
<p><strong>Step 4:</strong>The new divisor will be the<a>sum</a>of the dividend and quotient. Now we get 4n as the new divisor, and we need to find the value of n.</p>
5
<p><strong>Step 4:</strong>The new divisor will be the<a>sum</a>of the dividend and quotient. Now we get 4n as the new divisor, and we need to find the value of n.</p>
6
<p><strong>Step 5:</strong>The next step is finding 4n x n ≤ 62. Let us consider n as 1, now 41 x 1 = 41.</p>
6
<p><strong>Step 5:</strong>The next step is finding 4n x n ≤ 62. Let us consider n as 1, now 41 x 1 = 41.</p>
7
<p><strong>Step 6:</strong>Subtract 62 from 41, the difference is 21, and the quotient is 21.</p>
7
<p><strong>Step 6:</strong>Subtract 62 from 41, the difference is 21, and the quotient is 21.</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 add two zeroes to the dividend. Now the new dividend is 2100.</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 add two zeroes to the dividend. Now the new dividend is 2100.</p>
9
<p><strong>Step 8:</strong>Now we need to find the new divisor, which is 49 because 429 x 49 = 2101.</p>
9
<p><strong>Step 8:</strong>Now we need to find the new divisor, which is 49 because 429 x 49 = 2101.</p>
10
<p><strong>Step 9:</strong>Subtracting 2101 from 2100, we get the result -1.</p>
10
<p><strong>Step 9:</strong>Subtracting 2101 from 2100, we get the result -1.</p>
11
<p><strong>Step 10:</strong>Now the quotient is 21.49. Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero.</p>
11
<p><strong>Step 10:</strong>Now the quotient is 21.49. Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero.</p>
12
<p>So the square root of √462 ≈ 21.489</p>
12
<p>So the square root of √462 ≈ 21.489</p>
13
13