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 ?

Solution (By Examveda Team)

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
⇒ x² = (25k² + 30k + 9)
⇒ x² = 5 (5k² + 6k + 1) + 4
∴ On dividing x² by 5, we get 4 as remainder