Which number is bigger: $\sqrt[10]{2}$ or $1.2$? What is the general method for finding such inequalities? I have some more problems of this kind in the text I am using.

By the AM-GM Inequality,
$$\frac{2+1+1+1+1+1+1+1+1+1}{10} \geq \sqrt[10] 2$$
$$\frac{11}{10} \geq \sqrt[10] 2 \Rightarrow 1.2 \geq \sqrt[10] 2$$
The AM-GM inequality sometimes works when you have an n-th root but it depends on the problem.
