SOLUTION: what number is larger: a) sq rt of 7 or cube rt of 19. b) cube rt of 4 or 4th rt of 6. i really need some help with this.

Question 59008: what number is larger: a) sq rt of 7 or cube rt of 19. b) cube rt of 4 or 4th rt of 6. i really need some help with this.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
what number is larger:
a) sq rt of 7 or cube rt of 19.
7^(1/2) "compared to" 19^(1/3)
Raise both to the 6th power to get:
7^3 "compared to" 19^2
343 "compared to" 361"
Since these lines can be reversed
7^(1/2) < 19^(1/3)
-----------------------------
b) cube rt of 4 or 4th rt of 6.
4^(1/3) "compared to" 6^(1/4)
Raise both to the 12th power to get:
4^4 "compared to" 6^3
256 "compared to" 216
Therefore 4^(1/3)>6^(1/4)
Cheers,
Stan H.
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