simplify $\dfrac{10\sqrt{3}}{\sqrt{5}}$
4$\sqrt{15}$
2$\sqrt{15}$
2$\sqrt{5}$
4$\sqrt{5}$
Explanation:
$\dfrac{10\sqrt{3}}{\sqrt{5}}=\dfrac{10\sqrt{3}}{\sqrt{5}} \times \dfrac{\sqrt{5}}{\sqrt{5}}$ [using the rule $\dfrac{b}{\sqrt{a}}=\dfrac{b}{\sqrt{a}} \times \dfrac{\sqrt{a}}{\sqrt{a}}=\dfrac{b \sqrt{a}}{a}$]
=$\dfrac{10(\sqrt{15})}{5}$ [using the rule $\sqrt{a} \times \sqrt{b}=\sqrt{(a \times b)}$]
=2$\sqrt{15}$ [since $\dfrac{10}{5}=2$]
$\dfrac{10\sqrt{3}}{\sqrt{5}}=\dfrac{10\sqrt{3}}{\sqrt{5}} \times \dfrac{\sqrt{5}}{\sqrt{5}}$ [using the rule $\dfrac{b}{\sqrt{a}}=\dfrac{b}{\sqrt{a}} \times \dfrac{\sqrt{a}}{\sqrt{a}}=\dfrac{b \sqrt{a}}{a}$]
=$\dfrac{10(\sqrt{15})}{5}$ [using the rule $\sqrt{a} \times \sqrt{b}=\sqrt{(a \times b)}$]
=2$\sqrt{15}$ [since $\dfrac{10}{5}=2$]