For objective exams do:
Since we have a sqrt term, considering only perfect squares and those which are multiple of 2 as that can take care of log.
$T(2) = 1$//assume
$T(2^2) = T(2) + 1 = 2$
$T(2^{2^2}) = T(4) + 1 = 3$
$T\left(2^{2^3}\right) = T(16) + 1 = 4$
$T\left(2^{2^4}\right) = T(256) + 1 = 5$
So, we are getting $T(n) = \lg \lg n + 1 \implies T(n) = O(\log \log n)$