Question

RECOMPENSA: 40 pontos.

Gincana da noite:

Qual o resultado de:
$\sqrt[4]{2 \sqrt[3]{3 \sqrt{5} } }$

a)
$\sqrt[24]{30}$
b)
$\sqrt[24]{2880}$
c)
$\sqrt[26]{30}$
Boa sorte ksksks​

Answer 1

x=⁴√2 ³√3 ²√5

(x)⁴=(⁴√2 ³√3 ²√5)⁴

x⁴= 2 ³√3 ²√5

(x⁴)³= (2 ³√3 ²√5)³

x¹² = 2³.3.√5

(x¹²)² = (8.3.√5)²

x²⁴ = 24². 5

x²⁴ = 576. 5

x = ²⁴√2880

Answer 2

$\sqrt[4]{2 \sqrt[3]{3 \sqrt{5} } } \\ \sqrt[4]{2 \sqrt[3]{\sqrt{45} } } \\ \sqrt[4]{\sqrt[3]{8\sqrt{45} } }$

$\sqrt[4]{\sqrt[3]{\sqrt{2880} } } = \sqrt[24]{2880}$