Question

prove that 2
$+ \sqrt{3}$




​

Answer 1

To Prove: 2 + √3 is irrational

Let 2 + √3 is a rational number.

We know that we can write a rational number in the form of p/q. Where q ≠ 0.

So,

2 + √3 = p/q ( Where q ≠ 0 )

√3 = p/q - 2

Taking LCM

√3 = (p - 2q)/q

After solving it we will get

√3 = $\boxed{\bf{\frac{p - 2q}{q}}}$

√3 is an irrational number and we cannot write it in the form of p/q.

Hence, it contradicts the fact that √3 is irrational.

So , 2 + √3 is irrational .

Answer 2

Answer:

To Prove: 2+√3 is irrational

Let 2+√3 is a irrational number

__________________

2+√3 = p/q

√3 = p/q - 2

Taking LCM

√3 = ( p - 3q )/2

After solving it we will get

√3 = (p - 2q)/q

But √5 is an irrational number and we cannot write it in the form of p/q.

Hence, √5 is irrational.

So , 2+√3 is irrational .