# How do you simplify sqrt(8-x^2)?

Jun 18, 2017

$2 \sqrt{2} - x$

#### Explanation:

To simplify $\sqrt{8 - {x}^{2}}$ you can approach it as:

sqrt(8 & $\sqrt{- {x}^{2}}$

Since this isn't a perfect sqrt(8 you can break it down into:

$\sqrt{4} \times \sqrt{2}$

Since $\sqrt{4}$ is a perfect square we now get $2$
But we cannot break down $\sqrt{2}$ any further so we leave it how it is.
This is what we got now:

$2 \sqrt{2}$

As for $\sqrt{- {x}^{2}}$ it can be rewritten as:

${\left(- {x}^{\cancel{2}}\right)}^{\cancel{\frac{1}{2}}} = - x$

${\left(- {x}^{2}\right)}^{\frac{1}{2}} = - {x}^{\frac{2}{2}} = - x$

So our final answer is $2 \sqrt{2} - x$