30-second oral question

Question

The expression 9(2018^2)+20180+4040 is a square of what positive integer?

Answer 1

9(2018^2) + 20180 + 4040
= (3*2018)^2 + 10(2018) + 2(2018) + 4
= (3*2018)^2 + 12(2018) + 2^2
= (3*2018)^2 + 2*(3*2018)*2 + 2^2

Using a^2 + b^2 + 2ab = (a+b)^2, this is equal to:

= (3*2018 + 2)^2
= (6056)^2

Answer 2

Arora, nicely done, impressive!