Simplify by factoring

Question

Simplify by factoring. Assume that all variables under radicals  represent nonnegative, (Show all work)

√81x^6

Answer 1

Hi Theresa;

√81x⁶

 

If I understand correctly, the whole thing is being square-rooted.

square root of 81=9

square root of x³=x⁶

The latter is because (x³)(x³)=(x⁶)----3+3=6

 

You wanted factoring...

Assuming that it is all being square rooted, let's factor.

√81x⁶

√(9x³+0)(9x³+0)=(9x³+0)=9x³

 

Is this what you wanted?  Please let me know either way.

 

Answer 2

sqrt(81x^6)=sqrt(81)*sqrt(x^6)                   note: (x^a)*(x^a)=x^(a+a)=x^(2a)

                  =9*(x^3)

                  =9x^3