# How do you simplify sqrt(2b^5)/sqrt(14c^2)?

Apr 25, 2017

See below.

#### Explanation:

As you can see, you can't just directly take the square root and be done, or you wouldn't be simplifying correctly. Here is what I would do:

$\frac{\sqrt{2 {b}^{5}}}{\sqrt{14 {c}^{2}}}$

$\frac{\sqrt{2 b \cdot {b}^{2} \cdot {b}^{2}}}{\sqrt{14 \cdot c \cdot c}}$

$\frac{{b}^{2} \sqrt{2 b}}{c \sqrt{14}}$

$\frac{{b}^{2} \sqrt{2} \cdot \sqrt{b}}{c \cdot \sqrt{2} \cdot \sqrt{7}}$

$\frac{{b}^{2} \cdot \sqrt{b}}{c \cdot \sqrt{7}}$

$\frac{{b}^{2} \sqrt{b}}{c \sqrt{7}}$