Question Number 159839 by abelpedro last updated on 21/Nov/21
$${q}=\mathrm{2}\sqrt{\mathrm{2}\sqrt{\mathrm{2}}} \\ $$
Answered by abdullah_ff last updated on 21/Nov/21
$${q}\:=\:\mathrm{2}\sqrt{\mathrm{2}\sqrt{\mathrm{2}}} \\ $$$$=\:\mathrm{2}\sqrt{\mathrm{2}^{\mathrm{1}} \centerdot\mathrm{2}^{\frac{\mathrm{1}}{\mathrm{2}}} } \\ $$$$=\:\mathrm{2}\sqrt{\mathrm{2}^{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}} } \\ $$$$=\:\mathrm{2}\sqrt{\mathrm{2}^{\frac{\mathrm{3}}{\mathrm{2}}} } \\ $$$$=\:\mathrm{2}^{\mathrm{1}} \centerdot\mathrm{2}^{\frac{\mathrm{3}}{\mathrm{4}}} \\ $$$$=\:\mathrm{2}^{\frac{\mathrm{7}}{\mathrm{4}}} \\ $$