Question 186374


{{{sqrt(81*x^4)}}} Start with the given expression.



{{{sqrt(81*x^2*x^2)}}} Factor {{{x^4}}} into {{{x^2*x^2}}}. 



{{{sqrt(81)*sqrt(x^2)*sqrt(x^2)}}} Break up the square root using the identity {{{sqrt(A*B)=sqrt(A)*sqrt(B)}}}.



{{{9*sqrt(x^2)*sqrt(x^2)}}} Take the square root of {{{81}}} to get {{{9}}}.



{{{9*x*x}}} Take the square root of {{{x^2}}} to get {{{x}}}.



{{{9x^2}}} Multiply.


==================================================


Answer:



So {{{sqrt(81*x^4)}}} simplifies to {{{9x^2}}}



In other words, {{{sqrt(81*x^4)=9x^2}}} where "x" is non-negative.