# How do you simplify the expression sqrt(-8a^12b^5)?

$\sqrt{- 8 {a}^{12} {b}^{5}} = \sqrt{8 \cdot \left(- 1\right) {a}^{12} {b}^{5}} =$
remember that $\sqrt{x} = {x}^{\frac{1}{2}}$
$= 2 \sqrt{2} {a}^{\frac{12}{2}} {b}^{\frac{5}{2}} \sqrt{- 1}$
$= 2 \sqrt{2} {a}^{6} {b}^{\frac{5}{2}} i$
Where $i = \sqrt{- 1}$ is called immaginary unit.