Question

Multiply and write the answer in the simplest form.

(i) $3\sqrt{12}\times \sqrt{18}$ (ii) $3\sqrt{12}\times 7\sqrt{15}$

(iii) $3\sqrt{8}\times \sqrt{5}$ (iv) $5\sqrt{8}\times 2\sqrt{8}$

Answer 1

(i) $3\sqrt{12}\times \sqrt{18}=3\sqrt{4\times 3}\times \sqrt{9\times 2}=6\sqrt{3}\times 3\sqrt{2}=18\sqrt{6}$

(ii) $3\sqrt{12}\times 7\sqrt{15}=3\sqrt{4\times 3}\times 7\sqrt{15}=6\sqrt{3}\times 7\sqrt{15}=42\sqrt{45}=42\sqrt{9\times 5}=126\sqrt{5}$

(iii) $3\sqrt{8}\times \sqrt{5}=3\sqrt{4\times 2}\times \sqrt{5}=6\sqrt{2}\times \sqrt{5}=6\sqrt{10}$

(iv) $5\sqrt{8}\times 2\sqrt{8}=10\sqrt{64}=10\times 8=80$