Question

Efetue as radiciações, ou seja, transforme em um único radical:

a) √√7
b) √√√256
c) ³√2√5
d) √4³√15

Answer 1

$a) \sqrt{ \sqrt{7} } = (7^{\frac{1}{2}})^{\frac{1}{2}} = 7^{\frac{1}{4}} = \sqrt[4]{7}$

$b) \sqrt{\sqrt{ \sqrt{256} }}=\sqrt{\sqrt{ \sqrt{2^{8}} }}=(((2^{8})^{\frac{1}{2}})^{\frac{1}{2}})^\frac{1}{2}=2^{\frac{8}{8}} = 2^{1}= 2$

$c)\sqrt[3]{2\sqrt{5}} = \sqrt[3]{\sqrt{2^{2}.5}} = \sqrt[3]{\sqrt{20}} =\sqrt[3]{20^{\frac{1}{2}}} = (20^{\frac{1}{2}})^{\frac{1}{3}} = 20^{\frac{1}{6}} = \sqrt[6]{20}$

$d)\sqrt{4\sqrt[3]{15}} = \sqrt{\sqrt[3]{16.15}} = \sqrt[6]{240}$