Question

Express the following surds as mixed surds in the simplest form.

(i) $\sqrt{27}$

(ii) $\sqrt{50}$

(iii) $\sqrt[3]{40}$

(iv) $\sqrt[4]{32}$

(v) $\sqrt[5]{15625}$

Answer 1

(i) $\sqrt{27}=\sqrt{9}\times \sqrt{3}=3\sqrt{3}$

(ii) $\sqrt{50}=\sqrt{25}\times \sqrt{2}=5\sqrt{2}$

(iii) $\sqrt[3]{40}=\sqrt[3]{8}\times \sqrt[3]{5}=2\sqrt[3]{5}$

(iv) $\sqrt[4]{32}=\sqrt[4]{16}\times \sqrt[4]{2}=2\sqrt[4]{2}$

(v) $\sqrt[5]{15625}=\sqrt[5]{3125}\times \sqrt[5]{5}=5\sqrt[5]{5}$