Question

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

Answer 1

`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`