On dividing a number by 5, we get 3 as remainder. What will the remainder when the square of the this number is divided by 5 ?

Let the number be x and on dividing x by 5, we get k as quotient and 3 as remainder.

    x = 5k + 3

    x² = (5k + 3)²

   = (25k² + 30k + 9)

   = 5(5k² + 6k + 1) + 4

On dividing x² by 5, we get 4 as remainder.