Question

Simplify: $\sqrt{3}(\sqrt{5}+\sqrt{6})$.

Answer 1

$\sqrt{3}(\sqrt{5}+\sqrt{6})=(\sqrt{3}\times \sqrt{5})+(\sqrt{3}\times \sqrt{6})$ (using distributive law)
$=\sqrt{3\times 5}+\sqrt{3\times 6}$ (by using $\sqrt[n]{na}\times \sqrt[n]{nb}=\sqrt[n]{nab})$
$=\sqrt{15}+\sqrt{18}=\sqrt{15}+\sqrt{9\times 2}=\sqrt{15}+3\sqrt{2}$ .

$\therefore \sqrt{3}(\sqrt{5}+\sqrt{6})=\sqrt{15}+3\sqrt{2}$ .