When $$n$$ is divided by 5, remainder is 2 => $$n = 5k + 2$$     (k is quotient) Squaring both sides, we get : => $$n^2 = (5k + 2)^2$$ => $$n^2 = 25k^2 + 20k + 4$$ Now, if we divide $$n^2$$ by 5 => $$frac{25k^2 + 20k + 4}{5}$$ $$ecause$$ 25 and 20 are divided by 5 => Remainder = 4 Method II : When ‘n’ is divided by 5 the remainder is 2 Let n = 12 => $$n^2 = 12^2 = 144$$ Now, when 144 is divided by 5, => Remainder = 4