A) \[\sqrt{2}\]
B) \[2\sqrt{2}\]
C) \[11\sqrt{2}\]
D) \[9\sqrt{2}\]
Correct Answer: C
Solution :
[c] \[3\sqrt{2}+\sqrt[4]{16\times 4}+\sqrt[4]{625\times 4}+\sqrt[6]{{{2}^{3}}}\] \[=\sqrt{2}+\sqrt[4]{{{2}^{4}}\times {{2}^{2}}}+\sqrt[4]{{{5}^{4}}\times {{2}^{2}}}+\sqrt[6]{{{2}^{3}}}\] \[=3\sqrt{2}+2\sqrt[4]{{{2}^{2}}}+5\sqrt[4]{{{2}^{2}}}+\sqrt[6]{{{2}^{3}}}\] \[=3\sqrt{2}+2\sqrt{2}+5\sqrt{2}+\sqrt{2}\] \[=(3+2+5+1)\,\,\,\sqrt{2}=11\sqrt{2}\]
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