Simplify $\dfrac{2\sqrt{3}}{5}+\sqrt{108}$
$\dfrac{3 \sqrt{3}}{5}$
$\dfrac{32 \sqrt{3}}{5}$
$\dfrac{32 \sqrt{2}}{5}$
$\dfrac{32 \sqrt{3}}{15}$
Explanation:
$\dfrac{2\sqrt{3}}{5}+\sqrt{108}=\dfrac{2\sqrt{3}+5\sqrt{108}}{5}$ [find the LCD to add]
=$\dfrac{2\sqrt{3}+5(\sqrt{36}\times \sqrt{3})}{5}$ [using the rule $\sqrt{(a \times b)}=\sqrt{a} \times \sqrt{b}$]
=$\dfrac{2\sqrt{3}+30 \sqrt{3}}{5}$ [Evaluate \sqrt{36} and multiply to 5]
=$\dfrac{(2+30) \sqrt{3}}{5}$ [using the rule $a \sqrt{c}\pm b\sqrt{c}=(a \pm b) \sqrt{c}$]
=$\dfrac{32 \sqrt{3}}{5}$
$\dfrac{2\sqrt{3}}{5}+\sqrt{108}=\dfrac{2\sqrt{3}+5\sqrt{108}}{5}$ [find the LCD to add]
=$\dfrac{2\sqrt{3}+5(\sqrt{36}\times \sqrt{3})}{5}$ [using the rule $\sqrt{(a \times b)}=\sqrt{a} \times \sqrt{b}$]
=$\dfrac{2\sqrt{3}+30 \sqrt{3}}{5}$ [Evaluate \sqrt{36} and multiply to 5]
=$\dfrac{(2+30) \sqrt{3}}{5}$ [using the rule $a \sqrt{c}\pm b\sqrt{c}=(a \pm b) \sqrt{c}$]
=$\dfrac{32 \sqrt{3}}{5}$