# How do you simplify sqrt50+sqrt32-sqrt8?

Mar 20, 2017

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.

$\textcolor{red}{5 \sqrt{2}} + \textcolor{b l u e}{4 \sqrt{2}} - \textcolor{g r e e n}{2 \sqrt{2}}$

Simplify.

color(purple)(7sqrt2