Question

Prove that 2-√3 is irrational, given that √3 is irrational. ​

Answer 1

Answer:

Proof :-

Let

$2 - \sqrt{3}$

be rational.

Then,

$2 - \sqrt{3} = \frac{a}{b} \\ \sqrt{3} = \frac{a}{b} - 6 \\ \sqrt{3} = \frac{a - 6b}{b}$

Hence,

$\sqrt{3} \: is \: rational$

This is a contradiction arisen due to our incorrect assumption.

Therefore

$2 - \sqrt{3} \: is \: irrational$

Answer 2

$\mathfrak{\huge\underline{Answer:}}$

Given √3 is irrational number

Let 2 - √3 is rational number.

=> it should be in the form of p/q (fraction)

=> 2-√3 = p/q

= √3 = p/q + 2q/q

here √3 is irrational and p/q - 2q/q is an integer so it is a rational number.so it mean

irrational = rational

which contradict,

..our assumption is wrong and

2-√3 is irrational number.