Question

prove that 2-3 is irrational given that ^3 is irrational​

Answer 1

Answer:

$\bf\fbox\red[Question:-}$

prove that 2-3 is irrational given that ^3 is irrational

Let 2 - √3 be a rational number We can find co-prime a and b (b ≠ 0) such that 2 - √3 = abab 2−ab2−ab = √3 So we get, 2a−bb2a−bb = √3 Since a and b are integers, we get 2a−bb2a−bb is irrational and so √3 is rational. But √3 is an irrational number Which contradicts our statement Therefore 2 - √3 is irrational