Question

Q.1 Prove that 2+2V3 is an irrational number.​

Answer 1

Let us assume it is a rational number i.e x

x = 2 + 2√3x

x² = 4 + 12x² + 8√3x

(x² - 4 - 12x² ) x = 8√3

Here LHS is rational and RHS is irrational.

Hence our initial assumption was wrong and x is an irrational number.

Answer 2

Answer:

Hope it helps

Step-by-step explanation:

Let 2+v3 is a rational number.

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

2+v3=p/q

V3=p/q-2

V3=(p-2q)/q

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

But this contradicts the fact that v3 is an irrational number.

So,our supposition is false.

Therefore,2+/3 is an irrational number. Hence proved.