Question

prove that underoot 5 - 3 under root 2 is an irrational number​

Answer 1

Step-by-step explanation:

$let \: 5 - 3 \sqrt{2} \: be \: rational \: number$

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

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

p-5/q is a rational number

But 3root 2 is an irrational number

$5 - 3 \sqrt{2} \: is \: not \: equal \: to \: \frac{p}{q}$

.°. 5 - 3 root 2 is an irrational number