Question

Q-4.Prove that 5-4√3 is an irrational number.

Answer 1

Step-by-step explanation:

$let \: 5 - 4 \sqrt{3} \: be \: rational \: no. \\ 5 - 4 \sqrt{3} = \frac{p}{q} where \: pn \: q \: are \: co - prime \: integers$

$- 4 \sqrt{3} = \frac{p}{q} - 5 \\ - 4 \sqrt{3} = \frac{p - 5q}{q} \\ \sqrt{3} = \frac{p - 5q}{ - 4q}$

$for \: any \: value \: of \: p \: and \: q \: its \: value \: will \: be \: rational \:$

$but \: \sqrt{3} \: is \: irrational \\ so \: our \: assumption \: is \: wrong$

$therefore \: by \: contradiction \: 5 - 4 \sqrt{3} \: is \: irrational$

Answer 2

step by step explanation