Question 195063


{{{sqrt(144*x^10*y^12*z^18)}}} Start with the given expression.



{{{sqrt(144*x^2*x^2*x^2*x^2*x^2*y^12*z^18)}}} Factor {{{x^10}}} into {{{x^2*x^2*x^2*x^2*x^2}}}



{{{sqrt(144*x^2*x^2*x^2*x^2*x^2*y^2*y^2*y^2*y^2*y^2*y^2*z^18)}}} Factor {{{y^12}}} into {{{y^2*y^2*y^2*y^2*y^2*y^2}}}



{{{sqrt(144*x^2*x^2*x^2*x^2*x^2*y^2*y^2*y^2*y^2*y^2*y^2*z^2*z^2*z^2*z^2*z^2*z^2*z^2*z^2*z^2)}}} Factor {{{z^18}}} into {{{z^2*z^2*z^2*z^2*z^2*z^2*z^2*z^2*z^2}}}



{{{sqrt(144)*sqrt(x^2)*sqrt(x^2)*sqrt(x^2)*sqrt(x^2)*sqrt(x^2)*sqrt(y^2)*sqrt(y^2)*sqrt(y^2)*sqrt(y^2)*sqrt(y^2)*sqrt(y^2)*sqrt(z^2)*sqrt(z^2)*sqrt(z^2)*sqrt(z^2)*sqrt(z^2)*sqrt(z^2)*sqrt(z^2)*sqrt(z^2)*sqrt(z^2)}}} Break up the square root using the identity {{{sqrt(A*B)=sqrt(A)*sqrt(B)}}}.



{{{12*sqrt(x^2)*sqrt(x^2)*sqrt(x^2)*sqrt(x^2)*sqrt(x^2)*sqrt(y^2)*sqrt(y^2)*sqrt(y^2)*sqrt(y^2)*sqrt(y^2)*sqrt(y^2)*sqrt(z^2)*sqrt(z^2)*sqrt(z^2)*sqrt(z^2)*sqrt(z^2)*sqrt(z^2)*sqrt(z^2)*sqrt(z^2)*sqrt(z^2)}}} Take the square root of {{{144}}} to get {{{12}}}.



{{{12*x*x*x*x*x*sqrt(y^2)*sqrt(y^2)*sqrt(y^2)*sqrt(y^2)*sqrt(y^2)*sqrt(y^2)*sqrt(z^2)*sqrt(z^2)*sqrt(z^2)*sqrt(z^2)*sqrt(z^2)*sqrt(z^2)*sqrt(z^2)*sqrt(z^2)*sqrt(z^2)}}} Take the square root of {{{x^2}}} to get {{{x}}}.



{{{12*x*x*x*x*x*y*y*y*y*y*y*sqrt(z^2)*sqrt(z^2)*sqrt(z^2)*sqrt(z^2)*sqrt(z^2)*sqrt(z^2)*sqrt(z^2)*sqrt(z^2)*sqrt(z^2)}}} Take the square root of {{{y^2}}} to get {{{y}}}.



{{{12*x*x*x*x*x*y*y*y*y*y*y*z*z*z*z*z*z*z*z*z}}} Take the square root of {{{z^2}}} to get {{{z}}}.



{{{12x^5y^6z^9}}} Rearrange and multiply the terms.


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Answer:



So {{{sqrt(144*x^10*y^12*z^18)}}} simplifies to {{{12x^5y^6z^9}}}



In other words, {{{sqrt(144*x^10*y^12*z^18)=12x^5y^6z^9}}} where every variable is non-negative.