Question

Find the product.
(i) $\sqrt{3}\times \sqrt{7}$

(ii) $\sqrt[3]{11}\times \sqrt{10}$

(iii) $\sqrt[4]{12}\times \sqrt[7]{16}$

(iv) $\sqrt[3]{2}\times \sqrt[4]{3}$

(v) $\sqrt[3]{3}\times \sqrt[6]{2}$

Answer 1

$\left(\mathrm{i}\right)\sqrt{3}\times \sqrt{7}=\sqrt{3\times 7}=\sqrt{21}$

$\left(\mathrm{ii}\right)3\sqrt{11}\times \sqrt{10}=3\sqrt{11\times 10}=3\sqrt{110}$

$\left(\mathrm{iii}\right)4\sqrt{12}\times 7\sqrt{16}=4\times 7\sqrt{12\times 16}=28\sqrt{192}=28\sqrt{64\times 3}=28\sqrt{64}\times \sqrt{3}=28\times 8\times \sqrt{3}=224\sqrt{3}$

$\left(\mathrm{iv}\right)\sqrt[3]{2}\times \sqrt[4]{3}=\sqrt[3\times 4]{2^4}\times \sqrt[4\times 3]{3^3}=\sqrt[12]{16}\times \sqrt[12]{27}=\sqrt[12]{432}$

$\left(\mathrm{v}\right)\sqrt[3]{3}\times \sqrt[6]{2}=\sqrt[3\times 2]{3^2}\times \sqrt[6]{2}=\sqrt[6]{9}\times \sqrt[6]{2}=\sqrt[6]{18}$