multiplying sq rts

Question

sqrt18a^7b times sqrt27a^8b^6

I think I need to collect like terms such as the a's and b's. My big problem is order of operations. Every problem I do looks so different.

Answer 1

18 = 9 * 2 then sqrt 18 = 3sqrt2
sqrt a^7 = a^3 * sqrt a

27 = 9 * 3 then sqrt 27 = 3 sqrt3
sqrt a^8 = a^4
sqrt b^6 = b^3

Now just multiply the like-terms together.

Answer 2

3sqrt6 and sqrt2a^4

Answer 3

... 3sqrt6 and sqrt2a^4?

So you simplified the problem first as I said above and you get:

3(a^3)sqrt(2a) * 3(a^4)(b^3)sqrt(3)

and then you multiply those 2 things together and you get:

9(a^7)(b^3)sqrt(6a)