Question

Prove that 3 - 2√3 is an irrational number, if √3 is irrational.

Answer 1

Step-by-step explanation:

rational number can be written in the form of p/q. p,q are integers then (p-6q)/2q is a rational number. But this contradicts the fact that √3 is an irrational number. ... Therefore,3+2√3 is an irrational number.

Answer 2

Answer:

Hi friend,

Let 3-2√3 is a rational number.

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

3-2√3=p/q

√3=p/2q+3

√3=p+6q/2q

p,q are integers then (p-6q)/2q is a rational number.

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

So,our statement supposed is false.

Therefore,3+2√3 is an irrational number.

Step-by-step explanation: