I guessed this one correct but I would love to know an under 2min solution. Thanks so much.
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You can do it easily in 10 seconds if you observe the following exponent property:
1) sqrt(4) = 2
2) (number greater than 1)^(positive number) > 1.
In this case, 4 is greater than 1. Now,
The smallest value of (4)^(positive number) > 4^0 ,
And we know 4^0 = 1, hence both 4^(1/3) and 4^(1/4) are greater than 1.
So sum = 4^(1/2)+4^(1/3)+4^(1/4) > 2 + 1 + 1
=> sum > 4.
On a lighter note, this may be the first instance of an "eagle" helping a "fish"
Let me know if this helps
