# How do you simplify sqrt(-225x^8)?

May 22, 2015

By exponential rules, we know that ${a}^{\frac{n}{m}} = \sqrt[m]{{a}^{n}}$

Thus,

$\sqrt{- 225 {x}^{8}} = \sqrt[2]{- {225}^{1} \cdot {x}^{8}} = \left(- {225}^{\frac{1}{2}}\right) \left({x}^{\frac{8}{2}}\right) = {x}^{4} \sqrt{- \left({15}^{2}\right)}$

we have that ${i}^{2} = - 1$ and, thus, $\sqrt{- 1} = i$
${x}^{4} \sqrt{\left(- 1\right) \left({15}^{2}\right)} = {x}^{4} \sqrt{- 1} \sqrt{{15}^{2}} = \textcolor{g r e e n}{15 i {x}^{4}}$