A) \[{{2}^{1/4}}(3+\sqrt{2})\]
B) \[{{2}^{1/4}}(\sqrt{3}+\sqrt{2})\]
C) \[{{2}^{1/4}}(2+\sqrt{2})\]
D) \[{{2}^{1/4}}(\sqrt{3}+2)\]
Correct Answer: B
Solution :
Now,\[\sqrt{50}+\sqrt{48}=5\sqrt{2}+4\sqrt{3}\] \[=\sqrt{2}[5+2\cdot \sqrt{2}\cdot \sqrt{3}]\] \[=\sqrt{2}{{(\sqrt{3}+\sqrt{2})}^{2}}\] \[\therefore \] \[\sqrt{\sqrt{50}+\sqrt{48}}={{2}^{1/4}}(\sqrt{3}+\sqrt{2})\]
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