# Is this a typo in Section 1.8.1 Mathematics for Computer Science?

Am I completely mistake or is it suppose to say $$n^2$$ is a multiple of 2 and therefore $$n$$ must be a multiple of 4?

This is from MIT's Mathematics for Computer Science

• Generally: If $m,n$ are positive integers and $m^{1/n}$ is not an integer then $m^{1/n}$ is irrational. Proved by a similar method. – DanielWainfleet Apr 26 at 1:48
• What makes you think this is a mistake? – Servaes Apr 26 at 7:31

No, it is correct. The point is that $$2d^2=n^2$$ implies $$n^2$$ is even, and only even numbers square to give an even number, so $$n$$ much be even, so $$n^2$$ is then actually a multiple of $$4$$.
No. $$6^2$$ is a multiple of $$2$$ but $$6$$ is not a multiple of $$4$$. If $$n=2k$$ then for sure $$n^2=4k^2$$. So, MIT is right.