Question

Show that 5- √3 is irrational

Answer 1

Answer:

Let us assume that 5-√3 is rational

Than 5-√3=p/q  where q≠0

than

5-p/q = √3

5 q-p/q=√3

the above is saying that √3 is rational

But we know that √3 is irrational

∴our assumption is wrong

∴5-√3 is irrational

Answer 2

$hey \: mate \: here \: is \: your \: answer$

$suppose \: 5 - \sqrt{3} = \frac{p}{q} \: where \: p \: and \: q \: are \: co \: primes$

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

$since \: p \: and \: q \: are \: integer \: therefore \: \frac{ - p + 5}{q} \: is \: a \: rational \: number$

$so \: \sqrt{3} \: is \: also \: rational \: number$

$but \: \sqrt{3} \: is \: irrational \: number \:$

$this \: shows \: that \: our \: assumptiom \: is \: incorrect$

$so \: 5 - \sqrt{3} is \: an \: irrational \: number$

$hence \: prove$

$mark \: as \: brainlist$