Answer :
Final answer:
The remainder when the square of the number is divided by 9 is 0, as the other terms in the squared expression are multiples of 9 and do not affect the remainder.
Explanation:
Let's denote the number in question as x. Given that x divided by 36 leaves a remainder of 3, we can express this as x = 36k + 3 for some integer k. Squaring both sides of the equation yields x2 = (36k + 3)2 = 1296k2 + 216k + 9. When the square of the number is divided by 9, we are interested in the remainder of 1296k2 + 216k + 9 divided by 9. Notice that 1296k2 and 216k are multiples of 9 and will thus not affect the remainder. Only the term +9 matters, and 9 divided by 9 leaves a remainder of 0. Hence, when the square of the number is divided by 9, the remainder is 0.
