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Question Number 68740 by ahmadshah last updated on 15/Sep/19

Commented by Prithwish sen last updated on 15/Sep/19

$$\sqrt{30\sqrt{30\sqrt{30\sqrt{30}\sqrt{30{\left({30}^2\right)}^{\frac{1}{2}}}}}}$$$$=\sqrt{30\sqrt{30\sqrt{30\sqrt{30}\sqrt{{\left(30\right)}^2}}}}$$$$=\sqrt{30\sqrt{30\sqrt{{\left(30\right)}^{\frac{5}{2}}}}}$$$$=\sqrt{30\sqrt{30.{\left(30\right)}^{\frac{5}{4}}}}$$$$=\sqrt{30\sqrt{{\left(30\right)}^{\frac{9}{4}}}}$$$$=\sqrt{30.{\left(30\right)}^{\frac{9}{8}}}$$$$={\left({30}^{\frac{17}{8}}\right)}^{\frac{1}{2}}={30}^{\frac{17}{16}}$$

Answered by MJS last updated on 15/Sep/19

$${30}^{\frac{17}{16}}$$

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