Write $\sqrt{\dfrac{32}{144}}$ in the simplified form $a\sqrt{n}$
$\dfrac{\sqrt{32}}{3}$
$\dfrac{\sqrt{2}}{13}$
$\dfrac{\sqrt{2}}{3}$
$\dfrac{\sqrt{3}}{2}$
Explanation:
$\sqrt{\dfrac{32}{144}}=\dfrac{\sqrt{32}}{\sqrt{144}}$[using the rule $\sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}}$]
=$\dfrac{(\sqrt{16}\times \sqrt{2})}{12}$ [using the rule $\sqrt{(a \times b)}=\sqrt{a} \times \sqrt{b}$]
=$\dfrac{4 \sqrt{2}}{12}$ [simplify $\dfrac{4}{12}$]
=$\dfrac{\sqrt{2}}{3}$
$\sqrt{\dfrac{32}{144}}=\dfrac{\sqrt{32}}{\sqrt{144}}$[using the rule $\sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}}$]
=$\dfrac{(\sqrt{16}\times \sqrt{2})}{12}$ [using the rule $\sqrt{(a \times b)}=\sqrt{a} \times \sqrt{b}$]
=$\dfrac{4 \sqrt{2}}{12}$ [simplify $\dfrac{4}{12}$]
=$\dfrac{\sqrt{2}}{3}$