A number when divided by 6 leaves a remainder 3. When the square of the number is divided by 6, the remainder is ___.
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
x2=(6q+3)2.
⇒x2=36q2+36q+9
⇒ x2=6(6q2+6q+1)+3
∴ When x2 is divided by 6, the remainder is 3.