Question

Show that 4 - 3√2 is an irrational number.


PLEASE HELP ME TODAY IS MY EXAM

Answer 1

$Let \: \: ( 4 - 3 \sqrt{2} )\: \: be \: \: a \: \: rational \: \: number.</p><p>$

Then, It can be expressed as p/q.

So,

$4 - 3 \sqrt{2} = \frac{p}{q} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: 4 = \frac{p}{q} + 3 \sqrt{2}$

Here, A rational number (4) seems to be equated from the sum of a rational & irrational, which isn't possible. As the sum of a rational number & an irrational number is always an irrational number.

So, Our supposition was wrong.

Thus,

${ \large{ \red{(4 - 3 \sqrt{2}) \: \: is \: \:an \: \: irrational \: \: number.}}}$