比较根号5开5次方 根号3开3次方 根号2的大小

求思考过程!`
2024-11-23 09:31:45
推荐回答(1个)
回答1:

2^(1/2),3^(1/3),5^(1/5)
同时60次方
(2^(1/2))^60=2^30=(2^3)^10=8^10
(3^(1/3))^60=3^20=(3^2)^10=9^10 ==>2^(1/2)<3^(1/3)

2^30=(4^5)^3=1024^3
(5^(1/5))^60=5^12=(5^4)^3=625^3 ==>5^(1/5)<4^(1/4)

所以5^(1/5)<2^(1/2)<3^(1/3)