Question

If a numbers is divided by 6, the remainder is 3 then what will be the remainder when the square of the same numbers is divided by 6 again 

(1) 0 

(2) 1 

(3) 2 

(4) 3

Answer 1

(4) 3 

Let P be the number

p = 6q + 3

p² = (6q + 3)²

= 36q² + 36q + 9 = 36q² + 36q + 6 + 3

= 6(6q² + 6q + 1) + 3

∴ Remainder = 3