When ‘n’ is divided by 5 the remainder is 2. What is the remainder when $$n^2$$ is divided by 5 ?

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

=> $$\frac{25k^2 + 20k + 4}{5}$$

$$\because$$ 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