perplexus.info :: Numbers : Rational Result? Ridiculous!

Home > Numbers

Rational Result? Ridiculous! (Posted on 2004-12-20)

Can an irrational number, raised to an irrational power, give a rational result?

See The Solution Submitted by Old Original Oskar!

Rating: 2.7500 (4 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

Another answer

Comment 20 of 20 |

(In reply to answer by K Sengupta)

[EDIT]Let a = (v2)^v2

b= v2

It can be proved that a is an irrational number by advanced methods.

By elementary methods, it follows that: b is an irrational number.

Define c = a^b

Then, it follows that c= [(v2)^v2]^v2= (v2^)^2= 2, which is an integer, and therefore a rational number [/EDIT]

Edited on September 9, 2022, 2:14 am

Posted by K Sengupta on 2022-09-08 05:55:29

Please log in:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info