Question

Prove that 1/2+2√3 is an irrational number

Answer 1

Answer:

Let 1/2+√3 be a rational number.

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

1/2+√3=p/q

√3=p/q-1/2

√3=(2p-q)/2q

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

Then √3 is also a rational number.

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

So,our supposition is false.

Therefore,1/2+√3 is an irrational number