Comparing asymptotic running time of two algorithms $\sqrt n$ and $2^{\sqrt{\log _{2}n}}$
In order to compare two quantities/expression, it is often easier if they are in the same form. Here try expressing $t_a(n)$ as $2^{s_a(n)}$ and compare $s_a(n)$ with $\sqrt{\log_2 n}$.

Additionally, beware of using a program to check asymptotic comparisons: e.g. $f(n)=n^{10^6}$ and $g(n)=(1,0000000000000001)^n$