Question

Prove that 2+3√5 is an irrational number.​

Answer 1

Answer:

ANSWER IN THE ATTACHMENT.

Answer 2

◇answer◇

$Let x=2−3 \sqrt{5} \: be \: a \\ rational \: number.$

$3 \sqrt{5} =2−x$

$\huge\sqrt{5} =\frac{2−x}{3}$

Since x is rational, 2-x is rational and

$hence \: \frac{2−x}{3}\: is \: also \:rational \: number$

$⇒ \sqrt{5} \: is \: a \: rational \:numbers, \\ \: which \: is \: a\:contradiction.$

$Hence \: 2−3 \sqrt{5} \: must \: be \\ \: an \: irrational \: number.$