Question

Express the following as a mixed surd.
(i) $\sqrt{80}$ (ii) $\sqrt[3]{3256}$ (iii) $\sqrt[4]{41280}$ (iv) $\sqrt[5]{5320}$

Answer 1

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

(ii) $\sqrt[3]{3256}=\sqrt[3]{364\times 4}=\sqrt[3]{364}\sqrt[3]{34}$ $=\sqrt[3]{34^3}\sqrt[3]{34}=4\sqrt[3]{34}$

(iii) $\sqrt[4]{41280}=\sqrt[4]{4256\times 5}=\sqrt[4]{4256}\sqrt[4]{45}$ $=\sqrt[4]{44^4}\sqrt[4]{45}=4\sqrt[4]{45}$

(iv) $\sqrt[5]{5320}=\sqrt[5]{532\times 10}=\sqrt[5]{532}\sqrt[5]{510}$ $=\sqrt[5]{52^5}\sqrt[5]{510}=2\sqrt[5]{510}$