Question

prove that root 2 power root 2 is irrational .

Answer 1

yep

Answer 2

Well since root 2 is irrational, an irrational number raised to an irrational number should still be irrational.

Answer 3

But that's not always true. Hmm... Intresting. One moment.

Answer 4

Thing is, this is NOT an irrational number. It's rational.

Answer 5

Use proof by contradiction.

Answer 6

Assume is IS rational.

Answer 7

ok go on

Answer 8

i dont have a very nice method but i guess this will help you let's say \[x= 2 ^{\sqrt2}\] take log on both the sides \[\log x = \sqrt {2}\log2\] find the value of right side and finally \[X= e ^{\sqrt2 \log 2}\] and i am sure that would be irrational