How do you simplify #-4sqrt(7/8)#?

1 Answer
Apr 2, 2018

Answer:

The expression simplifies to #-sqrt14#.

Explanation:

#color(white)=-4sqrt(7/8)#

#=-4*sqrt(7/8)#

#=-4*sqrt7/sqrt8#

#=-4*sqrt7/sqrt(4*2)#

#=-4*sqrt7/(sqrt4*sqrt2)#

#=-4*sqrt7/(2*sqrt2)#

#=-4*sqrt7/(2*sqrt2)color(red)(*sqrt2/sqrt2)#

#=-4*(sqrt7*sqrt2)/(2*sqrt2*sqrt2)#

#=-4*(sqrt7*sqrt2)/(2*(sqrt2)^2)#

#=-4*(sqrt7*sqrt2)/(2*2)#

#=-4*(sqrt7*sqrt2)/(4)#

#=-color(red)cancelcolor(black)4*(sqrt7*sqrt2)/color(red)cancelcolor(black)(4)#

#=-sqrt7*sqrt2#

#=-sqrt14#

We can verify this answer using a calculator:

https://www.desmos.com/calculator

Hope this helped!