$\textit{Đáp án + Giải thích các bước giải:}$
$\text{a) $\sqrt{\dfrac{12}{270}}$ = $\dfrac{\sqrt{12}}{\sqrt{270}}$ = $\dfrac{\sqrt{4} . \sqrt{3}}{\sqrt{9} . \sqrt{30}}$ = $\dfrac{2\sqrt{3}}{3\sqrt{30}}$}$ $\text{= $\dfrac{2.\sqrt{3}.\sqrt{30}}{3\sqrt{30}.\sqrt{30}}$ = $\dfrac{6\sqrt{10}}{3.30}$ = $\dfrac{6\sqrt{10}:6}{90:6}$ = $\dfrac{\sqrt{10}}{15}$}$
$\text{b) $\sqrt{\dfrac{(2-\sqrt{3})^2}{75}}$ = $\dfrac{\sqrt{(2-\sqrt{3})^2}}{\sqrt{75}}$ = $\dfrac{\sqrt{(2 - \sqrt{3})^2}}{\sqrt{25}.\sqrt{3}}$ = $\dfrac{2 - \sqrt{3}}{5\sqrt{3}}$}$
$\text{= $\dfrac{(2 - \sqrt{3}) . \sqrt{3}}{5 . \sqrt{3} . \sqrt{3}}$ = $\dfrac{2\sqrt{3} - 3}{5 . 3}$ = $\dfrac{2\sqrt{3} - \sqrt{3} . \sqrt{3}}{15}$ = $\dfrac{\sqrt{3}(2-\sqrt{3})}{15}$}$
