# What is the square root of 125 times the cube root of 25?

It is

$\sqrt{125} \cdot {\left(25\right)}^{\frac{1}{3}} = 5 \cdot {5}^{\frac{1}{2}} \cdot {5}^{\frac{2}{3}} = 5 \cdot {5}^{\frac{1}{2} + \frac{2}{3}} = 5 \cdot {5}^{\frac{7}{6}} = 5 \cdot 5 \cdot {5}^{\frac{1}{6}} = 25 \cdot {5}^{\frac{1}{6}} = 25 \cdot \sqrt[6]{5}$