Question

Prove that 2 + √ is irrational number.​

Answer 1

Answer:

Let 2+√3 is a rational number.

A rational number can be written in the form of p/q.

2+√3= p/q.

√3=p/q-2

√3= (p-2q)/q

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

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

So, our supposition is false.

Therefore, 2+√3 is an irrational number.

Hence proved.

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