(x +3)^(2/3) = 8

Clear the fraction exponent, raise both sides to their 3rd powers,

[(x +3)^(2/3)]^3 = 8^3

(x +3)^2 = (2^3)^3

(x +3)^2 = 2^9

Take the square roots of both sides,

x +3 = 2^(4.5)

x = 2^(4.5) -3

x = (2^4)(sqrt(2)) -3

x = 16sqrt(2) -3 --------------answer.

by calculator,

x = 19.627417