Question

How to proved 5-2root 3 is a irrational number

Answer 1

Answer:

Given  5-2$\sqrt{3}$

Lets consider 5-2$\sqrt{3}$ as rational ie.,$\frac{p}{q}$

So,

5-2$\sqrt{3}$ = $\frac{p}{q}$

$\sqrt{3}$=$\frac{p}{q}x5-2$

$\sqrt{3}$=$\frac{p}{5q-2q}$

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

Hence lhs is irrational is

So our consideration is wrong

Hope u got ur answer