#(sqrt 5 - sqrt 7) (sqrt 5 - sqrt 8)# Multiply and Simplify?

1 Answer
Mar 3, 2018

Answer:

#(sqrt5-sqrt7)(sqrt5-sqrt8)=color(blue)(5-2sqrt10-sqrt35+2sqrt14#

Explanation:

#(sqrt5-sqrt7)(sqrt5-sqrt8)#

Use the FOIL method.
https://en.wikipedia.org/wiki/FOIL_method

#(sqrt5sqrt5)-(sqrt5sqrt8)-(sqrt5sqrt7)+(sqrt7sqrt8)#

Simplify.

#5-sqrt40-sqrt35+sqrt56#

Prime factorize the radicands.

#5-sqrt(2*2*2*5)-sqrt(5*7)+sqrt(2*2*2*7)#

Simplify.

#5-2sqrt10-sqrt35+2sqrt14#