${\left(3x\right)}^2=12$

eerste manier
$9x^2=12\iff x^2=\frac{4}{3}\iff x=\sqrt{\frac{4}{3}}$ of $x=\mathrm{‐}\sqrt{\frac{4}{3}}$,
$\sqrt{\frac{4}{3}}=\sqrt{4}\cdot \sqrt{\frac{1}{3}}=2\cdot \sqrt{\frac{3}{9}}=\frac{2}{3}\sqrt{3}$ , dus
$x=\frac{2}{3}\sqrt{3}$ of $x=\mathrm{‐}\frac{2}{3}\sqrt{3}$.

${\left(3x\right)}^2=12$

tweede manier
$3x=\sqrt{12}$ of $3x=\mathrm{‐}\sqrt{12}$, dus
$x=\frac{1}{3}\sqrt{12}=\frac{2}{3}\sqrt{3}$ of $x=\mathrm{‐}\frac{1}{3}\sqrt{12}=\mathrm{‐}\frac{2}{3}\sqrt{3}$

${\left(3x\right)}^2=11$

eerste manier
$9x^2=11$
$x=\sqrt{\frac{11}{9}}=\frac{1}{3}\sqrt{11}$ of $x=\mathrm{‐}\sqrt{\frac{11}{9}}=\mathrm{‐}\frac{1}{3}\sqrt{11}$

${\left(3x\right)}^2=11$

tweede manier
$3x=\sqrt{11}$ of $3x=\mathrm{‐}\sqrt{11}$, dus
$x=\frac{1}{3}\sqrt{11}$ of $x=\mathrm{‐}\frac{1}{3}\sqrt{11}$

${\left(\sqrt{3}x\right)}^2=12$

eerste manier
$3x^2=12$
$x^2=4$
$x=2$ of $x=\mathrm{‐}2$

${\left(\sqrt{3}x\right)}^2=12$

tweede manier
$\sqrt{3}x=\sqrt{12}$ of $\sqrt{3}x=\mathrm{‐}\sqrt{12}$
$x=\frac{\sqrt{12}}{\sqrt{3}}=\sqrt{4}=2$ of $x=\mathrm{‐}2$

${\left(\sqrt{3}x\right)}^2=16$

eerste manier
$3x^2=16$
$x^2=\frac{16}{3}$
$x=\sqrt{\frac{16}{3}}=4\sqrt{\frac{1}{3}}=\frac{4}{3}\sqrt{3}$ of $x=\mathrm{‐}\frac{4}{3}\sqrt{3}$

${\left(\sqrt{3}x\right)}^2=16$

tweede manier
$\sqrt{3}x=4$ of $\sqrt{3}x=\mathrm{‐}4$
$x=\frac{4}{\sqrt{3}}=\frac{4\sqrt{3}}{\sqrt{9}}=\frac{4}{3}\sqrt{3}$ of $x=\mathrm{‐}\frac{4}{3}\sqrt{3}$