Question

show that 5 - ✓3 is an irrational number ​

Answer 1

let we assume that 5 -√3 is rational number.

So, it can be written in the the form of a/b where we not is equal to zero and a and b are coprime.

$5 - \sqrt{3} = \frac{a}{b}$

$- \sqrt{3} = \frac{a}{b} - 5$

$- \sqrt{3} = \frac{a - 5b}{b}$

Therefore, and b is a integer a/b-5 is rational number so √3 will be rational.

But, our contradiction was wrong √3 is a irrational.

Hence, it is proved....