Question

What is the simplest form of 4 square root 81x^8y^5?

Answer 1

Firstly,
thanks for posting this.

81 = 9x9 or 9 squared so at this stage I'm guessing the last two. 
x^ 8 = (x^ 4) x (x^ 2) (its called the multiplication rule of indices). 
Okay I have approx 14 mins to answer.
No panic
√ 81.x^8 x √ y^5
√ (9x^2 x 9x^6) x √ y^5
= 9x x √ 9x^6 x  √ y^5
did I just gain time?
√ 9x^6 = √ 3x ^3 x √ 3x ^ 3
or 2 . √ 3x^3. √ y^5
more time
okay, so that wasnt successful. 
√ 9x^6 =√  (3x^2) x √ (3x^4)