Question Number 18551 by mondodotto@gmail.com last updated on 24/Jul/17
Answered by Tinkutara last updated on 24/Jul/17
$$\sqrt{{a}\sqrt{{a}\sqrt{{a}}}}\:=\:\sqrt{{a}\sqrt{{a}^{\frac{\mathrm{3}}{\mathrm{2}}} }}\:=\:=\sqrt{{a}^{\frac{\mathrm{7}}{\mathrm{4}}} }\:=\:{a}^{\frac{\mathrm{7}}{\mathrm{8}}} \\ $$$$\mathrm{Remember}:\:\sqrt{{a}\sqrt{{a}\sqrt{{a}\sqrt{{a}\sqrt{{a}...}}}}}\:=\:{a}^{\frac{\mathrm{2}^{{n}} \:−\:\mathrm{1}}{\mathrm{2}^{{n}} }} \\ $$$$\forall\:{n}\:\geqslant\:\mathrm{1},\:\mathrm{where}\:\mathrm{there}\:\mathrm{are}\:{n}\:\mathrm{square}\:\mathrm{roots}. \\ $$