Question

Express the following as a pure surd.
(i) $5\sqrt{6}$ (ii) $x\sqrt{x+y}$ (iii) $2\sqrt[3]{34}$

(iv) $3\sqrt[4]{45}$ (v) $a\sqrt[3]{3b^2}$

Answer 1

(i) $5\sqrt{6}=\sqrt{5^2}\sqrt{6}=\sqrt{25}\sqrt{6}=\sqrt{25\times 6}=\sqrt{150}$
(ii) $x\sqrt{x+y}=\sqrt{x^2}\sqrt{x+y}=\sqrt{x^2(x+y)}$
(iii) $2\sqrt[3]{34}=\sqrt[3]{32^3}\sqrt[3]{34}=\sqrt[3]{38\times 4}=\sqrt[3]{332}$
(iv) $3\sqrt[4]{45}=\sqrt[4]{43^4}\sqrt[4]{45}=\sqrt[4]{481}\sqrt[4]{45}=\sqrt[4]{481\times 5}=\sqrt[4]{4405}$
(v) $a\sqrt[3]{3b^2}=\sqrt[3]{3a^3}\sqrt[3]{3b^2}=\sqrt[3]{3a^3{b}^2}$