Question

Prove that √3 − √2 is an irrational number

Answer 1

Let √3 − √2 = r where r be a rational number 

Squaring both sides 

⇒ (√3-√2)²= r² 

⇒ 3 + 2 - 2 √6 = r² 

⇒ 5 - 2 √6 = r² 

 Here, 5 - 2√6 is an irrational number but r² is a rational number 

∴ L.H.S. ≠ R.H.S. 

 Hence it contradicts our assumption that √3 − √2 is a rational number.