Zero

Graphically, it can be seen that the two functions (LHS and RHS) never intersect, the closest approach being about 0.028 [Edited to corrected a typo from 0.28 to 0.028; which occurs if either x=0 or y=0 in each equation below)]

LHS is the same as x^2 + y^2 = 2 ; {y>=0}

RHS is the same as x^3 + y^3 = 3