Question

A number when divided by 5 leaves 3 as remainder. What will be the remainder if the square of this number is divided by 5 ?

Answer 1

let the number be x 

x=5k+3

x²=(5k+3)²

=(25k²+30k+9)

= 5(5k²+6k+1)+4

∴ the answer is 4 

dividing x² by 5 we will surely get 4 as remainder

Answer 2

There's an easy way to do this :
There's a property divisor*quotient+remainder = number
Now here wat u can do is :
5)N
----
3
Therefore 5*Q+ 3 ( q stands for quotient) always remember in such questions u can assume q to be 1 so the answer is =8 is your number
8^2 hence on dividing it by 5 gives you 4 as remainder
Hopefully you got the quick logic behind the question and was helpful too ...