How do you simplify -4sqrt(7/8)478?

1 Answer
Apr 2, 2018

The expression simplifies to -sqrt1414.

Explanation:

color(white)=-4sqrt(7/8)=478

=-4*sqrt(7/8)=478

=-4*sqrt7/sqrt8=478

=-4*sqrt7/sqrt(4*2)=4742

=-4*sqrt7/(sqrt4*sqrt2)=4742

=-4*sqrt7/(2*sqrt2)=4722

=-4*sqrt7/(2*sqrt2)color(red)(*sqrt2/sqrt2)=472222

=-4*(sqrt7*sqrt2)/(2*sqrt2*sqrt2)=472222

=-4*(sqrt7*sqrt2)/(2*(sqrt2)^2)=4722(2)2

=-4*(sqrt7*sqrt2)/(2*2)=47222

=-4*(sqrt7*sqrt2)/(4)=4724

=-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](useruploads.socratic.org)

Hope this helped!