0 added
0 removed
Original
2026-01-01
Modified
2026-02-28
1
<p>The long<a>division</a>method is particularly used for non-perfect square numbers. This method involves finding the closest perfect square number for the given number. Let us now learn how to find the<a>square root</a>of 103 using the long division method, step by step.</p>
1
<p>The long<a>division</a>method is particularly used for non-perfect square numbers. This method involves finding the closest perfect square number for the given number. Let us now learn how to find the<a>square root</a>of 103 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 103, we treat it as a single group because it has only three digits.</p>
2
<p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 103, we treat it as a single group because it has only three digits.</p>
3
<p><strong>Step 2:</strong>Now we need to find n whose square is closest to 10. We can say n is ‘3’ because 3 × 3 = 9, which is<a>less than</a>10. Now the<a>quotient</a>is 3, and after subtracting 9 from 10, the<a>remainder</a>is 1.</p>
3
<p><strong>Step 2:</strong>Now we need to find n whose square is closest to 10. We can say n is ‘3’ because 3 × 3 = 9, which is<a>less than</a>10. Now the<a>quotient</a>is 3, and after subtracting 9 from 10, the<a>remainder</a>is 1.</p>
4
<p><strong>Step 3:</strong>Bring down 3 next to the remainder, making it 13. Add the old<a>divisor</a>with the same number, 3 + 3, to get 6 as the new divisor.</p>
4
<p><strong>Step 3:</strong>Bring down 3 next to the remainder, making it 13. Add the old<a>divisor</a>with the same number, 3 + 3, to get 6 as the new divisor.</p>
5
<p><strong>Step 4:</strong>The new divisor is 6n. We need to find the value of n. Try n = 2, so 6 × 2 = 12, which is less than or equal to 13.</p>
5
<p><strong>Step 4:</strong>The new divisor is 6n. We need to find the value of n. Try n = 2, so 6 × 2 = 12, which is less than or equal to 13.</p>
6
<p><strong>Step 5:</strong>Subtract 12 from 13, and the remainder is 1. The quotient becomes 10.2.</p>
6
<p><strong>Step 5:</strong>Subtract 12 from 13, and the remainder is 1. The quotient becomes 10.2.</p>
7
<p><strong>Step 6:</strong>Since the<a>dividend</a>is less than the divisor, we need to add a decimal point and bring down two zeros, making the new dividend 100.</p>
7
<p><strong>Step 6:</strong>Since the<a>dividend</a>is less than the divisor, we need to add a decimal point and bring down two zeros, making the new dividend 100.</p>
8
<p><strong>Step 7:</strong>The new divisor will be 62. Try n = 1, so 62 × 1 = 62.</p>
8
<p><strong>Step 7:</strong>The new divisor will be 62. Try n = 1, so 62 × 1 = 62.</p>
9
<p><strong>Step 8</strong>: Subtract 62 from 100, leaving a remainder of 38.</p>
9
<p><strong>Step 8</strong>: Subtract 62 from 100, leaving a remainder of 38.</p>
10
<p><strong>Step 9:</strong>Continue doing these steps until we get the desired precision.</p>
10
<p><strong>Step 9:</strong>Continue doing these steps until we get the desired precision.</p>
11
<p>We find the square root of √103 ≈ 10.14889.</p>
11
<p>We find the square root of √103 ≈ 10.14889.</p>
12
12