Question

How do you simplify `5 sqrt 7 +12 sqrt 6 - 10 sqrt7 - 5 sqrt6`?

Answer 1

It is

#5 sqrt 7 +12 sqrt 6 - 10 sqrt7 - 5 sqrt6=sqrt6*(12-5)+sqrt7*(5-10)= 7*sqrt6-5*sqrt7#

Answer 2

`5sqrt 7+12sqrt 6-10sqrt 7-5sqrt 6=color(blue)(7sqrt6-5sqrt7)`

Explanation:

When adding or subtracting terms with square roots, you can only add or subtract terms with the same square root. It is similar to adding and subtracting numbers with variables such as `2a` or `3x`.

`5sqrt 7+12sqrt 6-10sqrt 7-5sqrt 6`

Gather like terms.

`12sqrt 6-5sqrt 6+5sqrt 7-10sqrt 7`

Simplify by adding or subtracting like terms as indicated.

`7sqrt6-5sqrt7`