Question

Qual valor de x, se x é igual a √√³√4096 ?

Answer 1

$x=\sqrt{\sqrt[3]{\sqrt{4096}}}$

Fatorar 4096 e multiplicar os índices

$x=\sqrt[2.3.2]{4096} \\ \\ x=\sqrt[12]{2^{12}} \\ \\ x=2$

Answer 2

$x=\sqrt{{\sqrt[3]{\sqrt{4096}}}}\\ \\ - Podemos \ reescrever \ da \ seguinte \ forma \ \\ \\ x= (4096)^{\frac{1}{2}*\frac{1}{3}*\frac{1}{2}}\\ \\ x=(4096)^{\frac{1}{2}}^2* \frac{1}{3}\\ \\ x=(4096)^\frac{1}{4}*\frac{1}{3}\\ \\ x=\sqrt[12]{4096}\\ \\ x= \sqrt[12]{2^{12}} \\ \\ x=2^{\frac{12}{12}}\\ \\ x=2$