Rewrite the square root of the division $\sqrt{\frac{75}{23}}$ as the division of square roots $\frac{\sqrt{75}}{\sqrt{23}}$.
$$\frac{\sqrt{75}}{\sqrt{23}}$$
Factor $75=5^{2}\times 3$. Rewrite the square root of the product $\sqrt{5^{2}\times 3}$ as the product of square roots $\sqrt{5^{2}}\sqrt{3}$. Take the square root of $5^{2}$.
$$\frac{5\sqrt{3}}{\sqrt{23}}$$
Rationalize the denominator of $\frac{5\sqrt{3}}{\sqrt{23}}$ by multiplying numerator and denominator by $\sqrt{23}$.
