Question

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

Answer 1

Let us consider 2- root 3 is rational.
2-root3=p/q. ( p and q are co primes and p is not equal to 0)
2=p/q +root 3


Root 3 is irrational and irrational plus rational give irrational.
In the above case then 2 is irrational. Which is wrong.
So our assumption was wrong and 2-root3 is irrational

Answer 2

Step-by-step explanation:

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

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.