Prove that 2-root 3 is irrational, given that root 3 is irrational
Prove that 2 – √ 3 is irrational, given that √3 is irrational
Let 2 – √3 be a rational number. Then there exist positive integers ‘a’ and ‘ b’, where a and b are integers having no common factor other than 1 and b ≠ 0 such that
Since a and b are integers, we get is rational. But it is already given that √3 is an irrational number.
This contradicts our assumption.
Hence, our assumption is wrong.
Therefore, is an irrational number.
Some other question: