Question

Express as a pure surd: $3\sqrt[4]{45}$

• A. $\sqrt[2]{2405}$
• B. $\sqrt[4]{445}$
• C. $\sqrt[4]{475}$
• D. $\sqrt[4]{4405}$

Answer 1

Answer: (D)

$\sqrt[4]{4405}$

A surd in which the whole of the rational number is under the radical sign and makes the radicand, is called pure surd.

$3\sqrt[4]{45}=\sqrt[4]{43^4}\times \sqrt[4]{45}=\sqrt[4]{481}\times \sqrt[4]{45}=\sqrt[4]{481\times 5}=\sqrt[4]{4405}$