### 4 Answers

Proof by counter-example:

Let a = 3 and b = 1/2, therefore a^b is the square root of 3, which can’t be written as a ratio of two whole numbers, and is therefore irrational.

let a = 2 and b = 1/2

a^b = 2^(1/2) = sqrt(2) which is not a rational number

Therefore the statement is false

Let a=2, b=1/2, both rational.

a^b = 2^(1/2)= sqrt 2 which is irrational.

Disproved.

yes

Source(s): Now answer my question… http://answers.yahoo.com/question/index;_ylt=Akauf…