Question-18551

Question Number 18551 by mondodotto@gmail.com last updated on 24/Jul/17

Answered by Tinkutara last updated on 24/Jul/17

\sqrt{a \sqrt{a \sqrt{a}}} = \sqrt{a \sqrt{a^{\frac{3}{2}}}} = = \sqrt{a^{\frac{7}{4}}} = a^{\frac{7}{8}}

Remember : \sqrt{a \sqrt{a \sqrt{a \sqrt{a \sqrt{a \dots}}}}} = a^{\frac{2^{n} - 1}{2^{n}}}

\forall n ⩾ 1, where there are n square roots .