Answer
$\frac{7}{2}-2\sqrt 2$
Work Step by Step
Step 1. Graph the functions as shown and we can identify intersections at $x=1,2$. The area of the enclosed region by the functions is the integral from $1$ to $2$.
Step 2. Evaluate
$A=\int_1^2(x-\frac{1}{\sqrt x})dx=(\frac{1}{2}x^2-2x^{1/2})|_1^2=(\frac{1}{2}(2)^2-2(2)^{1/2})-(\frac{1}{2}-2)=\frac{7}{2}-2\sqrt 2$
