Question

Prove that 2 root 3 minus 1 is an irrational number

Answer 1

Answer:

Step-by-step explanation:

Hi ,

Let us assume , to the contrary , that

2√3 - 1 is a rational ,

That is , we can find coprime

integers a and b ( b ≠ 0 ) such that

2√3 - 1 = a / b

2√3 = a / b + 1

2√3 = ( a + b ) / b

√3 = ( a + b ) / 2b

Since a and b are integers , we get

( a + b ) / 2b is rational , and so √3 is

rational .

But this contradicts the fact that √3

is irrational.

This contradiction has arisen

because of our incorrect assumption

that 2√3 - 1 is rational.

So , we conclude that 2√3 -1 is

irrational.