Question

Simplify:

$x^2$ is $94-42\sqrt{m}$
$m$ is

Answer 1

We rationalize the denominator,
$x=\frac{\sqrt{5}-1}{\sqrt{5}+2}\times \frac{\sqrt{5}-2}{\sqrt{5}-2}$
$x=\frac{5+2-3\sqrt{5}}{5-4}$
$x=\frac{7-3\sqrt{5}}{1}$
$x^2=(7-3\sqrt{5})(7-3\sqrt{5})$
$=49+9\ast 5-42\sqrt{5}$
$=94-42\sqrt{5}$