Simplifying with radicals

Question

In Algebra 1 I am given the following problem and told to simplify:

-5 √12 (7√6 - 4√8)

Please help me.

Answer 1

Here's ONE way:  -5 √12 (7√6 - 4√8) = -35√72 + 20√96 after distributing.

 

now, recognize that square root of 72 equals square root of (36•2) which is 6√2

and square root of 96 equals square root of (16•6) which is 4√6.

 

We get -35•6√2 + 20•4√6, or final answer -210√2 + 80√6.

 

Check this work (you could even check original expression decimally and this answer decimally--they should agree).