Simplifying with radicals

Question

In Algebra 1 I am given the following problem:

 

Simplify: 6√8 + 5√2 x 3√2 x 4√3

Please help me.

Answer 1

I'll rewrite your 6√8 + 5√2 x 3√2 x 4√3  as  6√8 + 5√2 •3√2 •4√3 because of my extreme dislike of the cross symbol for multiplication, which can be mistaken for the letter x, frequently used as the name of a variable (unknown) in Algebra.  Observe that √8 = 2√2.

 

6√8 + 5√2 •3√2 •4√3 = 6 •2√2 + 5•3•4•2•√3 by rearranging constant factors and replacing two square-root-of-2 factors by a constant factor 2.

 

Now, can you finish the job?