## mathslover Group Title prove that root 2 power root 2 is irrational . one year ago one year ago

1. Dido525 Group Title

|dw:1358647793062:dw|

2. mathslover Group Title

yep

3. Dido525 Group Title

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

4. Dido525 Group Title

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

5. Dido525 Group Title

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

6. Dido525 Group Title

7. Dido525 Group Title

Assume is IS rational.

8. mathslover Group Title

ok go on

9. ghazi Group Title

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

10. Dido525 Group Title

|dw:1358648074024:dw|

11. ghazi Group Title

you need to use calculator

12. Dido525 Group Title

|dw:1358648102171:dw|

13. Dido525 Group Title

|dw:1358648120754:dw|

14. Dido525 Group Title

This is obviously rational.

15. mathslover Group Title

^ two.. not 4

16. Dido525 Group Title

Right. Still rational though.

17. ghazi Group Title

there is a fallacy as far as i can see in your solution that you have missed square root on the exponent @djdo525

18. ghazi Group Title

sorry its Dido

19. mathslover Group Title

ok guys one correction, that root 2 power root 2 is rational . Sorry But prove that root 2 power root 2 is transcendental

20. mathslover Group Title

Also, PLEASE check whether it is transcendental or not , I am not sure. But I need your help.

21. ghazi Group Title

lol that was horrible

22. mathslover Group Title

OK friends I am totally confused. http://www.math.hmc.edu/funfacts/ffiles/30002.3-5.shtml Here I got that root 2 power root 2 is irrational..

23. mathslover Group Title

^ and as well as transcendental

24. dumbcow Group Title

@Dido525 , your example is incorrect, you showed (sqrt2)^(sqrt2)^sqrt2 is rational but sqrt2^sqrt2 is irrational

25. mathslover Group Title

yep

26. Dido525 Group Title

Yeah. That's what he wanted.