# How do you simplify sqrt(b^4c^5)?

Mar 2, 2018

${b}^{2} {c}^{\frac{5}{2}}$

#### Explanation:

Recall that $\sqrt{x} = {x}^{\frac{1}{2}} .$

Therefore,

$\sqrt{{b}^{4} {c}^{5}} = {\left({b}^{4} {c}^{5}\right)}^{\frac{1}{2}}$

Recall that ${\left(x y\right)}^{z} = {x}^{z} {y}^{z}$.

Therefore,

${\left({b}^{4} {c}^{5}\right)}^{\frac{1}{2}} = {b}^{4 \cdot \frac{1}{2}} \cdot {c}^{5 \cdot \frac{1}{2}} = {b}^{2} {c}^{\frac{5}{2}}$

Mar 3, 2018

sqrt(b^4  c^5  simplifies to   b^2  c^2 $\sqrt{c}$

#### Explanation:

Simplify   sqrt(b^4 c^5

1) Factor into perfect squares as far as possible

sqrt((b^2)^2  (c^2)^2 (c)

2) Find the square roots of the perfect squares, but leave the others inside

b^2 c^2 $\sqrt{c}$ $\leftarrow$ answer