By using the properties of definite integrals,evaluate the integral $\begin{align*}\int\limits_0^a\frac{\sqrt x}{\sqrt x+\sqrt{a-x}}dx \end{align*}$

Question

$\begin{array}{1 1}a \log 2 \\\frac{a}{2} \\ \frac{a}{2}\log 2 \\ \large\frac{a}{4} \end{array} $