Answer and Step-by-step explanation:
n > 0
n² divisible by 3 ⇒ n is divisible by 3.
Any number divisible by 3 has the sum of their components divisible by 3.
If n² is divisible by 3, we can say that n² can be written as 3*x.
n² = 3x ⇒ n = √3x
As n is a positive integer √3x must be a integer and x has to have a 3 factor. (x = 3.a.b.c...)
This way, we can say that x = 3y and y is a exact root, because n is a integer.
n² = 3x ⇒ n = √3x ⇒ n = √3.3y ⇒ n = √3.3y ⇒ n = √3²y ⇒ n = 3√y
Which means that n is divisible by 3.