Rewrite the square root of the division $\sqrt{\frac{456}{5}}$ as the division of square roots $\frac{\sqrt{456}}{\sqrt{5}}$.
$$\frac{\sqrt{456}}{\sqrt{5}}$$
Factor $456=2^{2}\times 114$. Rewrite the square root of the product $\sqrt{2^{2}\times 114}$ as the product of square roots $\sqrt{2^{2}}\sqrt{114}$. Take the square root of $2^{2}$.
$$\frac{2\sqrt{114}}{\sqrt{5}}$$
Rationalize the denominator of $\frac{2\sqrt{114}}{\sqrt{5}}$ by multiplying numerator and denominator by $\sqrt{5}$.
