Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I wonder if a square root of an irrational number is always irrational?

I would tend to think that yes, but I can´t think of any justification. Also there are cases which are rather hard to decide like sqrt(Pi).

share|improve this question
4  
The square of a rational number is rational, so the square root of an irrational number must be irrational. –  Daniel Fischer Sep 20 '13 at 18:29
    
Great answer. How come I didn´t think of this? :-D –  Adam Sep 20 '13 at 18:31

1 Answer 1

up vote 3 down vote accepted

Yes. The square of a rational is rational, so the identity $x = (\sqrt{x})^2$ tells us that if the square root is rational, the original number must be too.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.