Answer
The second root of $B$ is $A=\left[\begin{array}{ccc}{3} &{0} \\{0}& {2} \end{array}\right]$.
Work Step by Step
Let the matrix $A$ be given by
$$A=\left[\begin{array}{ccc}{3} &{0} \\{0}& {2} \end{array}\right].$$
Since $$A^2=\left[\begin{array}{ccc}{3} &{0} \\{0}& {2} \end{array}\right]\left[\begin{array}{ccc}{3} &{0} \\{0}& {2} \end{array}\right]=\left[\begin{array}{ccc}{9} &{0} \\{0}& {4} \end{array}\right]=B,$$
then the second root of $B$ is $A=\left[\begin{array}{ccc}{3} &{0} \\{0}& {2} \end{array}\right]$.