A number when divided by 6 leaves a remainder 3. When the square of the same number is divided by 6, the remainder is:
Answer: D
Let the number be N. Given, N = 6k + 3 for some integer k.
The square of the number is \(N^2 = (6k+3)^2 = (6k)^2 + 2(6k)(3) + 3^2\).
\(N^2 = 36k^2 + 36k + 9\).
\(N^2 = 36k^2 + 36k + 6 + 3 = 6(6k^2 + 6k + 1) + 3\).
This is in the form 6m + 3. So, when \(N^2\) is divided by 6, the remainder is 3.