Problem: n’th roots

Problem

True or false?

1. $\sqrt{a+b}=\sqrt{a}+\sqrt{b}$
2. $\sqrt{\sqrt[3]{a}}=a^{1/6}$
3. For $a>0, a^{1/3}⋅a^3=1$
4. For $a>0$ , $a^{-1/2}=1/\sqrt{a}$