how would I solve these?
the first one you can cross multiply
$\displaystyle x\sqrt{23} = 8\sqrt{6}$
$\displaystyle x=\frac{8\sqrt{6}}{\sqrt{23}}$
the second simlifies to
$\displaystyle \frac{x^2}{2}$
$\displaystyle \frac{\sqrt{3x^8}}{\sqrt{12x^2}}$
$\displaystyle \sqrt{\frac{3x^8}{12x^2}}$
$\displaystyle \sqrt{\frac{x^4}{4}}$
$\displaystyle \frac{x^2}{2}$
Edit: bigwave, it's not $\displaystyle \frac{x^3}{2}$, it's $\displaystyle \frac{x^2}{2}$