Question

Multiply:
(i) $3\sqrt{5}\mathrm{by}2\sqrt{5}$
(ii) $6\sqrt{15}\mathrm{by}4\sqrt{3}$
(iii) $2\sqrt{6}\mathrm{by}3\sqrt{3}$
(iv) $3\sqrt{8}\mathrm{by}3\sqrt{2}$
(v) $\sqrt{10}\mathrm{by}\sqrt{40}$
(vi) $3\sqrt{28}\mathrm{by}2\sqrt{7}$

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right)3\sqrt{5}\times 2\sqrt{5}=3\times 2\times \sqrt{5}\times \sqrt{5}=6\times 5=30 \\ \left(\mathrm{ii}\right)6\sqrt{15}\times 4\sqrt{3}=6\times 4\times \sqrt{5}\times \sqrt{3}\times \sqrt{3}=24\times 3\times \sqrt{5}=72\sqrt{5} \\ \left(\mathrm{iii}\right)2\sqrt{6}\times 3\sqrt{3}=2\times 3\times \sqrt{2}\times \sqrt{3}\times \sqrt{3}=6\times 3\times \sqrt{2}=18\sqrt{2} \\ \left(\mathrm{iv}\right)3\sqrt{8}\times 3\sqrt{2}=3\times 3\times \sqrt{2}\times \sqrt{2}\times \sqrt{2}\times \sqrt{2}=9\times 4=36 \\ \left(\mathrm{v}\right)\sqrt{10}\times \sqrt{40}=\sqrt{2}\times \sqrt{5}\times \sqrt{2}\times \sqrt{2}\times \sqrt{2}\times \sqrt{5}=\sqrt{2}\times \sqrt{2}\times \sqrt{2}\times \sqrt{2}\times \sqrt{5}\times \sqrt{5}=2\times 2\times 5=20 \\ \left(\mathrm{vi}\right)3\sqrt{28}\times 2\sqrt{7}=6\sqrt{7\times 4}\times \sqrt{7}=6\times 7\times \sqrt{4}=42\times 2=84 \end{gathered}$$