Q27 of 27 Page 1

Prove that 2-√3 is irrational, given that √3 is irrational.

Let 2 - √3 be a rational number


We can find co-primes a and b (b≠0) such that


2 - √3 = a/b


2 - a/b = √3


So we get, (2b - a)/b=√3


Since a and b are integers, (2b - a)/b is rational and so √3 should be rational. But √3 is an irrational number (Given).


Which contradicts our statement


Therefore 2 - √3 is irrational


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