How do you simplify #sqrt50+sqrt32-sqrt8#?

1 Answer
Mar 20, 2017

Answer:

#sqrt(50)+sqrt(32)-sqrt(8)=color(purple)(7sqrt2#

Explanation:

Simplify:

#sqrt(50)+sqrt(32)-sqrt(8)#

Terms with square roots can be added or subtracted only if their square roots are the same. Therefore, we need to simplify each term by prime factorization.

#color(red)(sqrt(50)=sqrt(2xx(5xx5))=5sqrt(2)#

#color(blue)(sqrt(32)=sqrt((2xx2)xx(2xx2)xx2)=4sqrt(2)#

#color(green)(sqrt(8)=sqrt((2xx2)xx2)=2sqrt(2)#

All terms now have the same square root and can now be added or subtracted.

#color(red)(5sqrt2) + color(blue)(4sqrt2) - color(green)(2sqrt2)#

Simplify.

#color(purple)(7sqrt2#