Question

Express the followings surds in its simplest form.
(i) $\sqrt[3]{332}$
(ii) $\sqrt{63}$
(iii) $\sqrt{243}$
(iv) $\sqrt[3]{3256}$.

Answer 1

(i) $\sqrt[3]{332}=\sqrt[3]{38\times 4}=\sqrt[3]{38}\times \sqrt[3]{34}=\sqrt[3]{32^3}\times \sqrt[3]{34}=2\sqrt[3]{34}$.
(ii) $\sqrt{63}=\sqrt{9\times 7}=\sqrt{9}\times \sqrt{7}=3\sqrt{7}$.
(iii) $\sqrt{243}=\sqrt{81\times 3}=\sqrt{81}\times \sqrt{3}=\sqrt{9^2}\times \sqrt{3}=9\sqrt{3}$.
(iv) $\sqrt[3]{3256}=\sqrt[3]{364\times 4}=\sqrt[3]{364}\times \sqrt[3]{34}=\sqrt[3]{34^3}\times \sqrt[3]{34}=4\sqrt[3]{34}$.