Single Choice

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

A$$(\sqrt{11}+1)\sqrt [ 4 ]{ 5 } $$
Correct Answer
B$$\sqrt [ 4 ]{ 5 }(1+\sqrt{5})$$
C$$\sqrt [ 4 ]{ 5 }(\sqrt{11}+\sqrt{5})$$
D$$\sqrt{5}(\sqrt{11}+1)$$

Solution

$$\sqrt{12\sqrt{5}+2\sqrt{55}}=\sqrt{12\sqrt{5}+2\sqrt{11}\sqrt{5}}$$
$$\Rightarrow \sqrt[4]{5}\sqrt{12+\sqrt[2]{11}}$$
$$\sqrt[4]{5}\sqrt{(\sqrt{11})^{2}+2\sqrt{11}+1^{2}}$$
$$\Rightarrow \sqrt[4]{5}\sqrt{(\sqrt{11}+1)^{2}}$$
$$\Rightarrow \boxed{(\sqrt{11}+1)\sqrt[4]{5}}$$

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