Question

prove that 5-3√2 is an irrational​

Answer 1

Answer:

sorry I no the answer please follow me

Answer 2

$\huge\red {\boxed {\mathfrak {☆AnSwEr☆}}}$

Let, us assume that $5-3\sqrt {2}$ is a rational number.

Such that, $5-3\sqrt {2}\:=\:\frac {p}{q}$where p and q are co-primes.

Rearranging the equation, we get :-

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

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

Since, p and q are co-primes, we get $\frac {p-5q}{q}$ is rational number and $\sqrt {3}$ is rational number.

But,

this contradicts the fact that $\sqrt {3}$ is irrational

This Contradiction has arisen because of our incorrect assumption that $5-\sqrt {3}$ is rational.

So, we conclude that$5-\sqrt {3}$ is irrational.