Question

Compare $2^{\frac{1}{2} }$ and $3^{\frac{1}{3} }$

Answer 1

2 1/2 plus 1 is 3 1/2. 3 1/2 is one number ahead.

Answer 2

Greetings from Brasil...

Before comparing mixed fractions, let's make them inappropriate

2 1/2 = 5/2

3 1/3 = 10/3

Comparing fractions. (MMC - Maximum Common Multiple - I don't know that term in English)

2 1/2 = 5/2 = 15/6

3 1/3 = 10/3 = 30/6

30/6 > 15/6  then

3 1/3 > 2 1/2