Question

Express the following surds as pure surds.

(i) $\sqrt[4]{5}$

(ii) $\sqrt[3]{6}$

(iii) $\frac{4}{3}\sqrt{6}$

(iv) $5\sqrt[3]{5}$

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

Answer 1

(i) $4\sqrt{5}=\sqrt{16}\times \sqrt{5}=\sqrt{80}$

(ii) $3\sqrt{6}=\sqrt{9}\times \sqrt{6}=\sqrt{54}$

(iii)$\frac{4}{3}\sqrt{6}=\sqrt{\frac{16}{9}}\times \sqrt{6}=\sqrt{\frac{96}{9}}=\sqrt{\frac{32}{3}}$

(iv) $5\sqrt[3]{5}=\sqrt[3]{125}\times \sqrt[3]{5}=\sqrt[3]{625}$

(v) $2\sqrt[4]{3}=\sqrt[4]{16}\times \sqrt[4]{3}=\sqrt[4]{48}$