| The value of \[\sqrt{2\sqrt[3]{4\sqrt{2\sqrt[3]{4}}}}...\] |
A) \[2\]
B) \[{{2}^{2}}\]
C) \[{{2}^{3}}\]
D) \[{{2}^{5}}\]
Correct Answer: A
Solution :
| \[x=\sqrt{2\sqrt[3]{4\sqrt{2\sqrt[3]{4}}}}\] |
| On squaring both side, \[{{x}^{2}}=2\cdot \sqrt[3]{4x}\] |
| Now, cubing both side |
| \[({{x}^{2}})=8\times 4x\] |
| \[\Rightarrow \] \[{{x}^{5}}=32\]\[\Rightarrow \]\[{{x}^{5}}={{(2)}^{5}}\] |
| \[\Rightarrow \] \[x=2\] |
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