Answer
(a) $46.3\space m^{2}/s^{2}$
(b) $40.1\space m^{2}/s^{2}$
Work Step by Step
(a) We can write,
$$\bar{v^{2}}=\frac{1}{3}(v_{1}^{2}+v_{2}^{2}+v_{3}^{2})$$
Let's plug known values into this equation.
$\bar{v^{2}}=\frac{1}{3}[(3\space m/s)^{2}+(7\space m/s)^{2}+(9\space m/s)^{2}]=46.3\space m^{2}/s^{2}$
(b) We can write,
$$(\bar{v})^{2}=[\frac{1}{3}(v_{1}+v_{2}+v_{3})]^{2}$$
Let's plug known values into this equation.
$(\bar{v})^{2}=[\frac{1}{3}(3\space m/s+7\space m/s+9\space m/s)]^{2}=40.1\space m^{2}/s^{2}$
