This problem is all about estimating values.

lets break it down by each 4.

4^1/2 = 2

4^1/3 = ?

you know 1^1/3 = 1 and 8^1/3 = 2

the cube root of 4 is some where b/w 1 and 2. Prefferably, it is somewhere around the 1.5 mark b/c 4 is halfway b/w 1 and 8

so we can approximate value of 4^1/3 ~ 1.5

4^1/4 = ?

you know 1^1/4 = 1 and 16^1/4 = 2

the 4th root of 4 lies some where b/w 1 and 2 again. This time 4 is closer to 1 than it is to 16, so we can approximate the value of 4^1/3 as ~ 1.1 or 1.2

so we have (2 + 1.5 + 1.1) which is collectively greater than 4.

(E)