Question

A number when divided by 6 leaves a remainder 3. When the square of the number is divided by 6, the remainder is ___.

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is C 3

Let the number be $x.$
When divided by 6, the number leaves a remainder 3.
Using Euclid's division lemma, this can be written as $x=6q+3,$ where $q$ is a natural number.

Squaring both sides, we get
$x^2=(6q+3{)}^2.$
$\Rightarrow x^2=36q^2+36q+9$
$\Rightarrow$ $x^2=6(6q^2+6q+1)+3$
$\therefore$ When $x^2$ is divided by 6, the remainder is 3.