For a reaction, the rate law expression is represented as follows 

Rate $=\mathrm{k}\left[\mathrm{A}\right]{\left[\mathrm{B}\right]}^{\frac{1}{2}}$

Interpret whether the reaction is elementary or complex. Give reason to support your answer.

In an elementary reaction order of reaction is equal to the molecularity. But molecularity should be integral.

From the given rate law, order of reaction is calculated as

$\frac{3}{2}\left[1+\frac{1}{2}\right]$

As molecularity cannot be fractional, therefore, order will not be equal to molecularity. Hence, the given rate law do not belong to an elementary reaction.