Question

Find sum of the following surds:
$(\sqrt{3}+\sqrt{2}),(2\sqrt{2}+3\sqrt{3}),(4\sqrt{2}-3\sqrt{3})$.

Answer 1

The sum of the given surds can be determined as follows:

$(\sqrt{3}+\sqrt{2})+(2\sqrt{2}+3\sqrt{3})+(4\sqrt{2}-3\sqrt{3})=(\sqrt{3}+3\sqrt{3}-3\sqrt{3})+(\sqrt{2}+2\sqrt{2}+4\sqrt{2})$

$=\sqrt{3}(1+3-3)+\sqrt{2}(1+2+4)=\sqrt{3}+7\sqrt{2}$

Hence, $(\sqrt{3}+\sqrt{2})+(2\sqrt{2}+3\sqrt{3})+(4\sqrt{2}-3\sqrt{3})=\sqrt{3}+7\sqrt{2}$.