Question

3. Decomponha o radicando em fatores primos e calcule as raízes:
b.
$\sqrt[4]{64}$
​

Answer 1

Olá,

64 | 2

32 | 2

16 | 2

8 | 2

4 | 2

2 | 2

1

$64 = 2 \times 2 \times 2 \times 2 \times 2 \times 2$

$64 = {6}^{4} \times {2}^{2}$

Logo:

$\sqrt[4]{64}$

$= \sqrt[4]{ {2}^{4} \times {2}^{2} }$

$= 2 \sqrt[4]{ {2}^{2} }$

$= 2 \sqrt[ \frac{4}{2} ]{ {2}^{ \frac{2}{2} } }$

$= 2 \sqrt{2}$