Question 148091
{{{sqrt((27y^3)/(z^4))}}} Start with the given expression.



{{{(sqrt(27y^3))/(sqrt(z^4))}}} Break up the root.



{{{(sqrt(3^2*3*y^2*y))/(sqrt(z^4))}}} Factor {{{27y^3}}} into {{{3^2*3*y^2*y}}}



{{{(sqrt(3^2*3*y^2*y))/(sqrt(z^2*z^2))}}} Factor {{{z^4}}} into {{{z^2*z^2}}}



{{{(sqrt(3^2)*sqrt(3)*sqrt(y^2)*sqrt(y))/(sqrt(z^2)*sqrt(z^2))}}} Break up the square roots.



{{{(3*sqrt(3)*y*sqrt(y))/(z*z)}}} Evaluate {{{sqrt(3^2)}}} to get 3. Evaluate {{{sqrt(y^2)}}} to get {{{y}}}. Evaluate {{{sqrt(z^2)}}} to get {{{z}}}. So the square root of anything squared is itself (assuming the variable is positive)




{{{(3y*sqrt(3y))/(z^2)}}} Multiply and combine the roots.



So {{{sqrt((27y^3)/(z^4))}}} simplifies to {{{(3y*sqrt(3y))/(z^2)}}}



In other words, {{{sqrt((27y^3)/(z^4))=(3y*sqrt(3y))/(z^2)}}} where every variable is positive and {{{z<>0}}}