Question

show that 2√3-1 is irrational no.

Answer 1

Hello friend

Here goes your answer

Let us assume 2√3-1 to be a rational number

A rational number is a one which can be expressed in the form p/q

So 2√3-1=p/q

For some integers p,q

2√3=(p/q)+1

2√3=2q+p/q

√3=2q-p/2q

As p,q are integers the RHS will be a rational number

So LHS also needs.to be a rational number

But this contradicts the fact that√3 is irrational. This contradiction has arisen due to our false assumption.

Therefore 2√3-1is irrational

Answer 2

Hey there !!

Lets assume that 2√3-1 is rational .

Let ,
2√3 - 1 =  r , where "r" is rational .

2√3 = r +1

√3 =  r +1 /2

here ,
its very clear that , RHS is purely rational.
But on the other hand , LHS is irrational.
This is a contradiction.
Hence ,
our assumption was wrong.

therefore ,
2√3-1 is irrational