Rational & Irrational Numbers...2

[nycmathguy]

(a) Give an example in which the result of raising an irrational number to an irrational power yields an irrational number.

(b) Give an example in which the result of raising an irrational number to a irrational power is a rational number.

 

[MathLover1]

a.
sqrt(2)^(sqrt(2)) we don‘t know whether is rational or irrational
but

and sqrt(2)^(1/3) is an irrational

b.

 

[nycmathguy]

a.
sqrt(2)^(sqrt(2)) we don‘t know whether is rational or irrational
but

and sqrt(2)^(1/3) is an irrational

b.

Interesting little problems from the David Cohen textbook.

Check this out:

Rational & Irrational Numbers