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Question -

Prove that 2 √3 – 1 is an irrational number. [CBSE 2010]



Answer -

Let 2 √3 – 1 is not an irrational number
and let 2 √3 – 1 a ration number
and then 2 √3 – 1 = a/b where a, b positive prime integers
 
√3 is a rational number
But √3 is an irrational number
Our supposition is wrong
2 √3 – 1 is an irrational number

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