Question

$\sqrt{12\sqrt{5}+2\sqrt{55}}=$...........

• A. $(\sqrt{11}+1)\sqrt[4]{45}$
• B. $\sqrt[4]{45}(1+\sqrt{5})$
• C. $\sqrt[4]{45}(\sqrt{11}+\sqrt{5})$
• D. $\sqrt{5}(\sqrt{11}+1)$

Answer 1

The correct option is A $(\sqrt{11}+1)\sqrt[4]{45}$

$\sqrt{12\sqrt{5}+2\sqrt{55}}=\sqrt{12\sqrt{5}+2\sqrt{11}\sqrt{5}}$

$\Rightarrow \sqrt[4]{45}\sqrt{12+\sqrt[2]{211}}$

$\sqrt[4]{45}\sqrt{(\sqrt{11}{)}^2+2\sqrt{11}+1^2}$

$\Rightarrow \sqrt[4]{45}\sqrt{(\sqrt{11}+1{)}^2}$

$\Rightarrow (\sqrt{11}+1)\sqrt[4]{45}$