Answer
The units of momentum are $\frac{kg \cdot m}{s}$
Work Step by Step
Let $u$ be the units of momentum. Then;
$\frac{u^2}{kg} = \frac{kg~m^2}{s^2}$
$u^2 = \frac{kg^2~m^2}{s^2}$
$u = \sqrt{\frac{kg^2~m^2}{s^2}}$
$u = \frac{kg \cdot m}{s}$
The units of momentum are $\frac{kg \cdot m}{s}$.