Question

Simplifique ( nao consegui digitar tudo)

Answer 1

Explicação passo-a-passo:

.

$a) \sqrt{ \sqrt{48} }$

$\sqrt[2 \times 2]{48}$

$\sqrt[4]{48}$

$\sqrt[4]{2 {}^{4} \times 3 }$

$\sqrt[4]{2 {}^{4} } \sqrt[4]{3}$

$\sqrt[4 \div 4]{2 {}^{4 \div 4} } \sqrt[4]{3}$

$2 \sqrt[4]{3}$

.

$b) \sqrt[3]{ \sqrt{128} }$

$\sqrt[3 \times 2]{128}$

$\sqrt[6]{128}$

$\sqrt[6]{2 {}^{7} }$

$\sqrt[6]{2 {}^{6 + 1} }$

$\sqrt[6]{2 {}^{6} \times 2 {}^{1} }$

$\sqrt[6]{2 {}^{6} \times 2}$

$\sqrt[6]{2 {}^{6} } \sqrt[6]{2}$

$\sqrt[6 \div 6]{2 {}^{6 \div 6} } \sqrt[6]{2}$

$2 \sqrt[6]{2}$

.

$c) \sqrt{ \sqrt{32} }$

$\sqrt[2 \times 2]{32}$

$\sqrt[4]{32}$

$\sqrt[4]{2 {}^{5} }$

$\sqrt[4]{2 {}^{4 + 1} }$

$\sqrt[4]{2 {}^{4} \times 2 {}^{1} }$

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

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

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

$2 \sqrt[4]{2}$

.

$d) \sqrt{ \sqrt[3]{25} }$

$\sqrt[2 \times 3]{25}$

$\sqrt[6]{25}$

$\sqrt[6]{5 {}^{2} }$

$\sqrt[6 \div 2]{5 {}^{2 \div 2} }$

$\sqrt[3]{5}$

.

$e) \sqrt{ \sqrt{ \sqrt{36} } }$

$\sqrt{ \sqrt{6} }$

$\sqrt[2 \times 2]{6}$

$\sqrt[4]{6}$

.

$f) \sqrt{ \sqrt{80} }$

$\sqrt[2 \times 2]{80}$

$\sqrt[4]{80}$

$\sqrt[4]{2 {}^{4} \times 5 }$

$\sqrt[4]{2 {}^{4} } \sqrt[4]{5}$

$\sqrt[4 \div 4]{2 {}^{4 \div 4} } \sqrt[4]{5}$

$2 \sqrt[4]{5}$

.

$g) \sqrt{ \sqrt{45} }$

$\sqrt[2 \times 2]{45}$

$\sqrt[4]{45}$

.

$h) \sqrt[3]{ \sqrt{512} }$

$\sqrt[3 \times 2]{512}$

$\sqrt[6]{512}$

$2 \sqrt[6]{2 {}^{3} }$

$2 \sqrt[6 \div 3]{2 {}^{3 \div 3} }$

$2 \sqrt{2}$

Answer 2

Oie, tudo bom?

a)

$= \sqrt{ \sqrt{48} } \\ = \sqrt[2 \: . \: 2]{48} \\ = \sqrt[4]{48} \\ = \sqrt[4]{2 {}^{4} \: . \: 3 } \\ = \sqrt[4]{2 {}^{4} } \sqrt[4]{3} \\ \boxed{ = 2 \sqrt[4]{3} }$

b)

$= \sqrt[3]{ \sqrt{128} } \\ = \sqrt[3 \: . \: 2]{128} \\ = \sqrt[6]{128} \\ = \sqrt[6]{2 {}^{7} } \\ = \sqrt[6]{2 {}^{6 + 1} } \\ = \sqrt[6]{2 {}^{6} \: . \: 2 {}^{1} } \\ = \sqrt[6]{2 {}^{6} \: . \: 2} \\ = \sqrt[6]{2 {}^{6} } \sqrt[6]{2} \\ \boxed{ = 2 \sqrt[6]{2} }$

c)

$= \sqrt{ \sqrt{32} } \\ = \sqrt[2 \: . \: 2]{32} \\ = \sqrt[4]{32} \\ = \sqrt[4]{2 {}^{5} } \\ = \sqrt[4]{2 {}^{4 + 1} } \\ = \sqrt[4]{2 {}^{4} \: . \: 2 {}^{1} } \\ = \sqrt[4]{2 {}^{4} \: . \: 2 } \\ = \sqrt[4]{2 {}^{4} } \sqrt[4]{2} \\ \boxed{ = 2 \sqrt[4]{2} }$

d)

$= \sqrt{ \sqrt[3]{25} } \\ = \sqrt[2 \: . \: 3]{25} \\ = \sqrt[6]{25} \\ = \sqrt[6]{5 {}^{2} } \\ \boxed{ = \sqrt[3]{5} }$

e)

$= \sqrt{ \sqrt{ \sqrt{36} } } \\ = \sqrt{ \sqrt{ \sqrt{6 {}^{2} } } } \\ = \sqrt{ \sqrt{6} } \\ = \sqrt[2 \: . \: 2]{6} \\ = \boxed{ \sqrt[4]{6} }$

f)

$= \sqrt{ \sqrt{80} } \\ = \sqrt[2 \: . \: 2]{80} \\ = \sqrt[4]{80} \\ = \sqrt[4]{2 {}^{4} \: . \: 5} \\ = \sqrt[4]{2 {}^{4} } \sqrt[4]{5} \\ \boxed{ = 2 \sqrt[4]{5} }$

g)

$= \sqrt{ \sqrt{45} } \\ = \sqrt[2 \: . \: 2]{45} \\ \boxed{ = \sqrt[4]{45} }$

h)

$= \sqrt[3]{ \sqrt{512} } \\ = \sqrt[3 \: . \: 2]{512} \\ = \sqrt[6]{512} \\ = \sqrt[6]{2 {}^{9} } \\ = \sqrt[6]{2 {}^{6 + 3} } \\ = \sqrt[6]{2 {}^{6} \: . \: 2{}^{3} } \\ = \sqrt[6]{2 {}^{6} } \sqrt[6]{2 {}^{3} } \\ = 2 \sqrt[6]{2 {}^{3} } \\ \boxed{ = 2 \sqrt{2} }$

Att. NBA YoungBoy