# How do you simplify sqrt(16-x^2)?

Jul 27, 2015

You cannot really simplify this, but you way want to rewrite.

#### Explanation:

Since $16 - {x}^{2} = \left(4 - x\right) \left(4 + x\right)$ you can write:

$= \sqrt{\left(4 - x\right) \left(4 + x\right)}$ or:

$= \sqrt{4 - x} \cdot \sqrt{4 + x}$

This will only work if $- 4 \le x \le + 4$, otherwise $16 - {x}^{2}$ will be negative = not allowed.