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Question -

Prove that 2 – 3 √5 is an irrational number. [CBSE 2010]



Answer -

Let 2 – 3 √5 is not an irrational number and let 2 – 3 √5 is a rational number
Let 2 – 3 √5 = a/b where a and b are positive prime integers
 
⟹2b−a3b=√5
√5 is a rational
But √5 is an irrational number
Our supposition is wrong
2 – 3 √5 is an irrational

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