Question

Prove that V x,y ∈ R+ `(x+y)^(1/n)` ≤ `x^(1/n)` + `y^(1/n)` ?

Answer 1

See below.

Explanation:

We know using the binomial expansion that

`(x^(1/n)+y^(1/n))^n = x + g(x,y)+y` with `g(x,y) ge 0` then

`(x+y)^(1/n) le x^(1/n)+y^(1/n)`