Rewrite the square root of the division $\sqrt{\frac{450}{19}}$ as the division of square roots $\frac{\sqrt{450}}{\sqrt{19}}$.
$$173\times \frac{\sqrt{450}}{\sqrt{19}}$$
Factor $450=15^{2}\times 2$. Rewrite the square root of the product $\sqrt{15^{2}\times 2}$ as the product of square roots $\sqrt{15^{2}}\sqrt{2}$. Take the square root of $15^{2}$.
$$173\times \frac{15\sqrt{2}}{\sqrt{19}}$$
Rationalize the denominator of $\frac{15\sqrt{2}}{\sqrt{19}}$ by multiplying numerator and denominator by $\sqrt{19}$.
