Question

prove that 2 root 3 minus root 5 is an irrational number​

Answer 1

$\underline\bold{\huge{SOLUTIONS\::}}$

Let

$2 \sqrt{3} - 5$

be a rational no.So, it can be expressed

in the form p and q where p and q has no

common factor other than 1and q is not

zero.

So,

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

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

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

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

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

But this Contradict the fact that it is a

rational no.because √3 is not a rational

no.

Hence 2√3-5 is a irrational no .