Question

show that 2
$\sqrt{3}$
-1 irrational

Answer 1

Let √3-1 be a rational number.

So, √3-1 = p/q, q≠0

=> √3 = p/q+1

=> √3 = p+q/q = integer/integer

=> √3 = a rational number

which contradicts the fact that √3 is irrational.


Hence, √3-1 is an irrational number.