# Math Help - proof help please?

Let a be an integer. Prove that a^2 is divisible by 5 if and only if a is divisible by 5.

Now use that result to prove that there does not exist a rational number whose square is 5.

Say $5\not | a$ then $\gcd(a,5)=1$. But we are told that $5|(a\cdot a)$ with $\gcd(a,5)=1$ thus $a|5$ a contradiction.