Show that `root3(2) > root5(3)`

Show that root(3)(ax^(2)+by^(2)+cz^(2))=root(3)(a)+root(3)(b)+root(3)(c ) , if ax^(3)=by^(3)=cz^(3) and (1)/(x)+(1)/(y)+(1)/(z)=1 .

Which one of root(3)(2), root(4)(3), root(6)(5) and root(12)(26) is greatest?

root(5)(root(4)(3^2))

The value of (root(3)(3.5) + root(3)(2.5)) { (root(3)(3.5) )^2 - root(3) (8.75) + ( root(3)(2.5))^2} is

root(3)(135)-:root(3)(5)

Write the following in the descending order of magnitude. root3(2), sqrt(3),root6(5)