Answer
The result follows by the Intermediate Value Theorem.
Work Step by Step
Since the function $ x^2$ is continuous on $[0,1]$ and $ f(0)=0\neq f(1)=1$, thus $0.5 $ is between $ f(0)$ and $f(1)$. Then, by the Intermediate Value Theorem, the function $x^2$ takes the value $0.5$ for some $x\in (0,1)$.
