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Question

Prove that (231) is an irrational number.

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Solution

Let (231) be a rational number.

A rational number can be written in the form of pq where p,q are integers.

231=pq

23=pq+1

23=p+qq

3=p+q2q

p,q are integers then p+q2q is a rational number.

Then,3 is also a rational number.

But this contradicts the fact that 3 is an irrational number.

Therefore, our supposition is false.

So,231 is an irrational number.


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