Now, for any real number greater than 1, it's n-th root is always greater than 1. Why is so?
Say, b is the n-th root of a.
Therefore, a = b*b* ... *b (n times)
- (1) if b < 1; b*b is always smaller than b. Thus b*b* ... *b (n times) is smaller than b. Hence, a < 1.
(2) if b > 1; b*b is always greater than b. Thus b*b* ... *b (n times) is greater than b. Hence, a > 1.
Therefore,
- (1) cube root(4) > 1
(2) fourth root(4) > 1
The correct answer is E.
