Question

Simplify :

(7root 3oot 10 + root 3) - (2root 5 root 6 + root 5 ) - (3root 2 root 15 + 3root 2)

Answer 1

Considering the given expression as $\left(7\sqrt{3}\times \sqrt{10}+\sqrt{3}\right)-\left(2\sqrt{5}\times \sqrt{6}+\sqrt{5}\right)-\left(3\sqrt{2}\times \sqrt{15}+3\sqrt{2}\right)$
$$\begin{gathered} =\left(7\sqrt{30}+\sqrt{3}\right)-\left(2\sqrt{30}+\sqrt{5}\right)-\left(3\sqrt{30}+3\sqrt{2}\right) \\ =7\sqrt{30}+\sqrt{3}-2\sqrt{30}-\sqrt{5}-3\sqrt{30}-3\sqrt{2} \\ =2\sqrt{30}+\sqrt{3}-\sqrt{5}-3\sqrt{2} \end{gathered}$$