Question

$\sqrt{10}\times \sqrt{15}=?$
(i) $\sqrt{25}$
(ii) $5\sqrt{6}$
(iii) $6\sqrt{5}$
(iv) None of these

Answer 1

$$\begin{gathered} \sqrt{10}\times \sqrt{15} \\ =\sqrt{2\times 5}\times \sqrt{3\times 5} \\ =\sqrt{2}\times \sqrt{5}\times \sqrt{3}\times \sqrt{5}\left[\sqrt{ab}=\sqrt{a}\times \sqrt{b}\right] \end{gathered}$$
$$\begin{gathered} =5\times \sqrt{2\times 3} \\ =5\sqrt{6} \end{gathered}$$
Hence, the correct answer is option (ii).