1.

Prove that √3 − √2 is an irrational number

Answer»

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 - 26 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. 



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