Question

how to show that number is any rational number​

Answer 1

Answer:

we can show it by contradiction method..

Answer 2

Assume that,

$\sf 4\sqrt{2}  is \: a \: rational \: number.$

Then, there exists coprime positive integers p & q such that

$\sf 4\sqrt{2} = \frac{p}{q}$

$\sf \sqrt{2} = \frac{p}{4_q} (∵ \: p \: and \: q \: are \: integers)$

$\sf ⇒\frac{p}{4_q} \: is \: rational$

$\sf ⇒ \sqrt{2} \: is \: rational \:$

$\sf This \: contradict \: the \: fact \: that  \sqrt{2}$

$\sf \: is \: irrational. \: so \: our \: assumption \: is \: incorrect.$

$\sf \: Hence \: \: 4\sqrt{2} \: is \: irrational$