Answer
See below.
Work Step by Step
The units for $k$ are $N/m$. Expand the definition of newtons to get $N/m=\frac{kg \times m}{s^2\times m}=\frac{kg}{s^2}$. The units for mass are kilograms (kg). Substitute these units to get $$\sqrt{\frac{k}{m}}=\sqrt{\frac{kg\times m}{kg \times s^2\times m}}=\sqrt{\frac{1}{s^2}}=\frac{1}{s}=s^{-1}$$
