The expectation value of $x$ in the state ${1\over\sqrt{2}}(u_0+u_1)$.

$$\begin{eqnarray*} {1\over 2}\left\langle u_0+u_1\left\vert x\right\vert u_0+u_1\... ...\hbar\over 8m\omega}(1+1) \\ &=&\sqrt{\hbar\over 2m\omega} \\ \end{eqnarray*}$$