Solving T(n) = 3T(n/3)+sqrt(n) in terms of or O notions using master method

Question

Please help me solve it in terms of Theta or Big O

Answer 1

Based on the Wikipedia article I would say it is $\theta(n)$. Case 1.

https://en.wikipedia.org/wiki/Master_theorem_(analysis_of_algorithms)#Generic_form

$a=b=3$ and $c_{crit} = 1$. $f(n)$ has exponent $c=\frac 1 2$ since $f(n)={\sqrt n}=n^\frac 1 2$. So, $T(n)=\theta(n)$ by Case 1 because $c < c_{crit}$.

Bobby