Question

prove that 2√3-4 is an irrational number

Answer 1

2_/3 - 4 is irrational as 2_/3 is irrational and irrational subtracted from rational is irrational.

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Answer 2

Hi there !

Lets assume that 2√3-4 is rational number

Let , 
2√3-4 = r , where r is a rational no:

2√3 = r + 4
√3  = r + 4/2

Here ,
RHS is purely rational
But , LHS is irrational

This is a contradiction.

Hence , our assumption was wrong.

Therefore ,
2√3-4 is an irrational number