Question

怎样比较大小2^(1/2)和3^(1/6)和5^(1/8)?

Answer 1

2^(1/2)=8^(1/6)所以大于3^(1/6)

2^(1/2)=16^(1/8)所以大于5^(1/8)

3^(1/6)＝81^(1/24)

5^(1/8)=75^(1/24)

所以3^(1/6)>5^(1/8)

故2^(1/2)>3^(1/6)>5^(1/8)