Question

On dividing a number by $5$, we get $3$ as remainder. What will the remainder when the square of this number is divided by $5$?

• A. $0$
• B. $1$
• C. $2$
• D. $4$

Answer 1

The correct option is D $4$

Let the number be $x$ and on dividing $x$ by $5$, we get $k$ as quotient and $3$ as remainder.
$\therefore$ $x=5k+3$
$\Rightarrow$ $x^2={(5k+3)}^2$
$=(25k^2+30k+9)$
$=5(5k^2+6k+1)+4$
$\therefore$ On dividing $x^2$ by $5$, we get $4$ as remainder.