Calculate the Time complexity
The answer depends on the initial value. For example, if $T(0) = 2$ then you can prove by induction that $T(n) = 2$ for all $n$. More generally, let $S(n) = T(n)/2$. Then
$$
S(n) = \frac{T(n)}{2} = \frac{\sqrt{2T(n-1)}}{2} = \sqrt{\frac{T(n-1)}{2}} = \sqrt{S(n-1)}.
$$
Simple induction now shows that $S(n) = \sqrt[2^n]{S(0)}$, and so
$$ T(n) = 2 \sqrt[2^n]{\frac{T(0)}{2}}. $$
In particular, this shows that $T(n) \to 2$.

We can estimate the speed of convergence using the estimate
$$
\sqrt[2^n]{x} = \exp \frac{\log x}{2^n} = 1 + O\left(\frac{\log x}{2^n}\right).
$$
This shows that
$$ T(n) = 2 + O(2^{-n}). $$