What is the returns to scale of the production function q = min {K, L^(1/2)}?
You have a Leontief production function and in optimum you will always have $K=\sqrt{L}=q_1$.  Now increase both inputs by factor $k&gt;1$ and you arrive at $k*K &gt; \sqrt{kL}=q_2$ where the first inequality follows from $k&gt;\sqrt{k}$ for $k&gt;1$ and the second ineqality from the fact that only the minimum matters in your production function.
Therefore you have $F(kK,kL)= \sqrt{kL}&lt;kK=k\sqrt{L} =k*F(K,L)$ with any optimal input combination $(K,L)$ and therefore decreasing returns to scale.