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

1 Answer
Jun 18, 2017

Answer:

#2sqrt2-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)xxsqrt(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:

#2sqrt2#

As for #sqrt(-x^2)# it can be rewritten as:

#(-x^cancel2)^(cancel(1/2))=-x#

#(-x^2)^(1/2)=-x^(2/2)=-x#

So our final answer is #2sqrt2-x#