If 1 < x < 9/8, which is bigger, ∛3x or √2x.

Answer 1

at the lower end , that is, at x = 1
3^(1/3) = 1.44..
√2 = 1.414.. so ∛3x > √2x

at x = 9/8
(27/8)^(1/3) = 3/2 = 1.5
√(18/8) = √(36/16) = 6/4 = 1.5

so for all values for 1 < x < 9/8
∛3x > √2x

They become equal at x = 9/8

as a matter of fact, ∛3x > √2x for 0 < x < 9/8

http://www.wolframalpha.com/input/?i=plot+y+%3D+%E2%88%9B(3x)+,+y+%3D+%E2%88%9A(2x)