Question

Resolva as operações ( não consegui digitar )

Answer 1

Oie, tudo bom?

a)

$= 3 \sqrt{5} + 7 \sqrt{5} \\ = (3 + 7) \sqrt{5} \\ \boxed{ = 10 \sqrt{5} }$

b)

$= \sqrt[3]{a} + 2 \sqrt[3]{a} - 4 \sqrt[3]{a} \\ = 1 \sqrt[3]{a} + 2 \sqrt[3]{a} - 4 \sqrt[3]{a} \\ = (1 + 2 - 4) \sqrt[3]{a} \\ = (3 - 4) \sqrt[3]{a} \\ = - 1 \sqrt[3]{a} \\ \boxed{ = - \sqrt[3]{a} }$

c)

$= \sqrt{45} + \sqrt{90} \\ = \sqrt{3 {}^{2} \: . \: 5 } + \sqrt{3 {}^{2} \: . \: 10} \\ = \sqrt{3 {}^{2} } \sqrt{5} + \sqrt{3 {}^{2} } \sqrt{10} \\ \boxed{ = 3 \sqrt{5} + 3 \sqrt{10} }$

d)

$= 2 \sqrt{7} \sqrt{5} \\ = 2 \sqrt{7 \: . \: 5} \\ \boxed{ = 2 \sqrt{35} }$

e)

$= \sqrt[3]{2} \sqrt[4]{b {}^{2} } \\ = \sqrt[12]{2 {}^{4} } \sqrt[12]{(b {}^{2} ) {}^{3} } \\ = \sqrt[12]{2 {}^{4} } \sqrt[12]{b {}^{6} } \\ = \sqrt[12]{2 {}^{4} b {}^{6} } \\ \boxed{ = \sqrt[12]{16b {}^{6} } }$

f)

$= \sqrt[3]{20} \div \sqrt[3]{10} \\ = \sqrt[3]{20 \div 10} \\ \boxed{ = \sqrt[3]{2} }$

g)

$= \sqrt[3]{14} \div \sqrt[6]{7 {}^{2} } \\ = \sqrt[6]{14 {}^{2} } \div \sqrt[6]{7 {}^{2} } \\ = \sqrt[6]{14 {}^{2} \div 7 {}^{2} } \\ = \sqrt[6]{2 {}^{2} } \\ \boxed{ = \sqrt[3]{2} }$

h)

$= ( \sqrt[5]{3 {}^{2} } ) {}^{3} \\ = \sqrt[5]{(3 {}^{2}) {}^{3} } \\ = \sqrt[5]{3 {}^{6} } \\ = \sqrt[5]{3 {}^{5 + 1} } \\ = \sqrt[5]{3 {}^{5} \: . \: 3 {}^{1} } \\ = \sqrt[5]{3 {}^{5} \: . \: 3 } \\ = \sqrt[5]{3 {}^{5} } \sqrt[5]{3} \\ \boxed{ = 3 \sqrt[5]{3} }$

i)

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

j)

$= \sqrt{ \sqrt[7]{x} } \\ = \sqrt[2 \: . \: 7]{x} \\ \boxed{ = \sqrt[14]{x} }$

Att. NLE Top Shotta

Answer 2

Explicação passo-a-passo:

.

$a)3 \sqrt{5} + 7 \sqrt{5}$

$(3 + 7) \sqrt{5}$

$10 \sqrt{5}$

.

$b) \sqrt[3]{a} + 2 \sqrt[3]{a} - 4 \sqrt[3]{a}$

$(1 + 2 - 4) \sqrt[3]{a}$

$(3 - 4) \sqrt[3]{a}$

$- \sqrt[3]{a}$

.

$c) \sqrt{45} + \sqrt{90}$

$\sqrt{3 {}^{2} \times 5 } + \sqrt{3 {}^{2} \times 10 }$

$\sqrt{3 {}^{2} } \sqrt{5} + \sqrt{3 {}^{2} } \sqrt{10}$

$\sqrt[2 \div 2]{3 {}^{2 \div 2} } \sqrt{5} + \sqrt[2 \div 2]{3 {}^{2 \div 2} } \sqrt{10}$

$3 \sqrt{5} + 3 \sqrt{10}$

.

$d)2 \sqrt{7} \times \sqrt{5}$

$2 \sqrt{7 \times 5}$

$2 \sqrt{35}$

.

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

$\sqrt[12]{2 {}^{4} } \sqrt[12]{b {}^{6} }$

$\sqrt[12]{2 {}^{4}b {}^{6} }$

$\sqrt[12]{16b {}^{6} }$

.

$f) \sqrt[3]{20} \div \sqrt[3]{10}$

$\sqrt[3]{20 \div 10}$

$\sqrt[3]{2}$

.

$g) \sqrt[3]{14} \div \sqrt[6]{7 {}^{2} }$

$\sqrt[6]{14 {}^{2} } \div \sqrt[6]{7 {}^{2} }$

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

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

$\sqrt[3]{2}$

.

$h)( \sqrt[5]{3 {}^{2} } ) {}^{3}$

$\sqrt[5]{3 {}^{2 \times 3} }$

$\sqrt[5]{3 {}^{6} }$

$\sqrt[5]{3 {}^{5 + 1} }$

$\sqrt[5]{3 {}^{5} \times 3 {}^{1} }$

$\sqrt[3]{3 {}^{5} \times 3 }$

$\sqrt[5]{3 {}^{5} } \sqrt[5]{3}$

$\sqrt[5 \div 5]{3 {}^{5 \div 5} } \sqrt[5]{3}$

$3 \sqrt[5]{3}$

.

$i) \sqrt{ \sqrt{6} }$

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

$\sqrt[4]{6}$

.

$j) \sqrt{ \sqrt[7]{x} }$

$\sqrt[2 \times 7]{x}$

$\sqrt[14]{x}$