Prove that 2 root under 3 - 1 is an irrational number

1.	Prove that 2 root under 3 - 1 is an irrational number
Answer» if your Q is 2√3-1 then,Let 2√3-1 be rational number say p/q where q is not equal to zero and p and q are coprime.2√3-1=p/q2√3=p/q+1√3=p+q/2q√3is irrational and p+q/2q is rational.But rational is not equal to irrational. Therefore 2√3-1 is irrational. 2√3-12√2Let 2√2 be rational number say p/q where q is not equal to zero and p&q are coprime.2√2=p/q√2=p/q÷2√2 is irrational and p/q÷2 is rational.But rational is not equal to irrational.Therefore 2√2 is irrational. Let 2√3-1 is rational , let a and b is the positive integer , 2√3-1=a/b , 2√3=a/b+1 , 2√3= a+b/b , √3=a+b/2b , so our assumption was wrong , hence 2√3-1 is irrational

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