Question

prove that 5 - √3 is an irrational number​

Answer 1

Answer:

let 5-√3 is rational number the it form of p/ q the substrate by 5 both side we get √3 is do not equal to p/ q - 5 here our contridation is wrong 5 -√3 is an irrational number. please thanks me

Answer 2

Suppose 5 - √3 is rational number i.e,

$5 - \sqrt{3} = \frac{p}{q} \\ \\ 5 - \frac{p}{q} = \sqrt{3} \\ \\ \frac{5q - p}{q} = \sqrt{3}$

LHS is rational but RHS is irrational which is a contradiction.

So, our supposition is wrong and hence 5 - √3 is an irrational number.

Hope it helps