Question

Prove that 2√3-1 is an irrational number

Answer 1

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here is your answer
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2√3-1 is irrational

PROOF:

An irrational number is non recurring and cannot be represented in a fractional form.

so,

The value of 2√3 = 3.4641016151377...

Thus, 3.4641016151377... + 1 = 4.4641016151377...

Thus, proved that 2√3 + 1 is irrational.
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Answer 2

Let 2√3-1 be a rational number.

A rational number can be written in the form of p/q where p,q are integers.

2√3-1=p/q
2√3=p/q+1
2√3=(p+q)/q
√3=(p+q)/2q

p,q are integers then (p+q)/2q is a rational number.

Then,√3 is also a rational number.

But this contradicts the fact that √3 is an irrational number.

Therefore, our supposition is false.

So,2√3-1 is an irrational number.