Solve G_{n}=n^2/sqrt{n^3+4n}

$$G _ { n } = \frac { n ^ { 2 } } { \sqrt { n ^ { 3 } + 4 n } }$$

Solve for G_n (complex solution)

$$G_{n}=\left(n\left(n^{2}+4\right)\right)^{-\frac{1}{2}}n^{2}$$

$$n\neq -2i\text{ and }n\neq 2i\text{ and }n\neq 0$$

Solve for G_n

$$G_{n}=\frac{n^{\frac{3}{2}}}{\sqrt{n^{2}+4}}$$

$$n>0$$