simplifying with radicals

Question

In Algebra 1 I am given the following problem:

 

Simplify: 6√8 + 5√12 x 3√2 x 4√3

Please help me.

Answer 1

6√8 + 60√72 = 6√8 + 60√9√8

 

                    = 6√8 + 180√8

 

                    = 186√8

 

                    = 186√4√2 

 

                    =372√2

Answer 2

note that a√b x c√d = ab√cd
and a√b + c√b = (a+c)√b

 

6√8 + 5√12 x 3√2 x 4√3 = 6√4.2 + 5√4.3 x 3√2 x 4√3

= 6.2√2 + 5.2.√3  x 3√2 x 4√3  

=12√2 +10√3 x 3√2 x 4√3 

 

 

we should do the multiplication first, then addition :

 

12√2 +10.3.4√3.3.2 = 12√2 +120.3√2 = 12√2 +360√2 = 372√2