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Simplify by factoring

Simplify by factoring. Assume that all variables under radicals  represent nonnegative, (Show all work)
√81x^6

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Vivian L. | Microsoft Word/Excel/Outlook, essay composition, math; I LOVE TO TEACHMicrosoft Word/Excel/Outlook, essay comp...
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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.
 
Arthur D. | Effective Mathematics TutorEffective Mathematics Tutor
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sqrt(81x^6)=sqrt(81)*sqrt(x^6)                   note: (x^a)*(x^a)=x^(a+a)=x^(2a)
                  =9*(x^3)
                  =9x^3