Question

Prove that $\tt{2\sqrt{3}-1}$ is an irrational number.​

Answer 1

Answer:

To prove: 2√3-1 is an irrational number.

Proof:

Let us assume that 2√3 -1 is a rational number.

So, it can be written in the form a/b

2√3-1= a/b

Here a and b are coprime numbers and b ≠ 0

Solving 2√3-1 = a/b we get,

=>2√3 = a/b +1

=>√3= a+b/2b

This shows (a+b)/2b is a rational number. But we know that √3 is an irrational number.

So, it contradicts our assumption. Our assumption of 2√3-1 is a rational number is incorrect.

2√3-1 is an irrational number

Hence proved