Simplifying radicals

Question

In Algebra 1 I am given the following problem:

 

Simplify: -5√12 (7√6 - 4√8)

 

Please help me.

Answer 1

-5√2 (7√6 - 4√8)

(-5√2)(7√6) - (-5√2)(4√8)        distribute

-35√12 + 20√16

 

Can you simplify the radicals?

Answer 2

Alright, James, when we multiply two things under a radical, they multiply and stay under the radical.

 

-5√2(7√6 - 4√8)

-35√12 + 20√16

 

We can then break down what's under the radical.

 

-35√(4(3)) + 20√16

 

Since the square root of 4 is 2, it comes out front. The square root of 16 is 4.

 

-70√3 + 80

 

Boom.