Question

Me ajudem a resolver a 5,6 e 7

Answer 1

5)

a)

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

b)

$\sqrt[5]{ {7}^{10} } = \sqrt[5 \div 5]{ {7}^{10 \div 5} } = {7}^{2} = 49$

c)

$\sqrt[8]{ {7}^{6} } = \sqrt[8 \div 2]{ {7}^{6 \div 2} } = \sqrt[4]{ {7}^{3} }$

d)

$\sqrt[12]{ {2}^{3} . {a}^{6} } = \sqrt[12]{ {2}^{3} } . \sqrt[12]{ {a}^{6} } = \\ \sqrt[12 \div 3]{ {2}^{3 \div 3} } . \sqrt[12 \div 6]{ {a}^{6 \div 6} } = \sqrt[4]{2}. \sqrt{a}$

e)

$\sqrt[15]{ {5}^{10} } = \sqrt[15 \div5 ]{ {5}^{10 \div 5} } = \sqrt[3]{ {5}^{2} } = \sqrt[3]{25}$

f)

$\sqrt[6]{ {a}^{2}. {b}^{2} } = \sqrt[6]{ {(ab)}^{2} } = \sqrt[6 \div 2]{ {(ab)}^{2 \div 2} } \\ \sqrt[3]{ab}</p><p>6)</p><p>a) </p><p>[tex] \sqrt[8]{64} = \sqrt[8]{ {2}^{6} } = \sqrt[8 \div 2]{ {2}^{6 \div 2} } = \sqrt[4]{ {2}^{3} } \\ = \sqrt[4]{8}$

b)

$\sqrt[10]{625} = \sqrt[10]{ {5}^{4} } = \sqrt[10 \div 2]{5^{4 \div 2} } = \sqrt[5]{ {5}^{2} } \\ = \sqrt[5]{25}$

c)

$\sqrt[20]{243} = \sqrt[20]{ {3}^{5} } = \sqrt[20 \div 5]{ {3}^{5 \div 5} } = \sqrt[4]{3}$

d)

$\sqrt[14]{128} = \sqrt[14]{ {2}^{7} } = \sqrt[14 \div 7]{ {2}^{7 \div 7} } = \sqrt{2}$

7)

a)

$\sqrt{ \sqrt{5} } = \sqrt[2.2]{5} = \sqrt[4]{5}$

b)

$\sqrt[5]{\sqrt[2]{13} } = \sqrt[5.2]{13} = \sqrt[10]{13}$

c)

$\sqrt[3]{ \sqrt{7} } = \sqrt[3.2]{7} = \sqrt[6]{7}$

d)

$\sqrt[5]{ \sqrt[6]{11} } = \sqrt[5.6]{11} = \sqrt[30]{11}$

e)

$\sqrt[3]{ \sqrt[]{ \sqrt[5]{4} } } = \sqrt[3.2.5]{4} = \\ \sqrt[30]{4} = \sqrt[30]{ {2}^{2} } = \sqrt[15]{2}$

f)

$\sqrt{ \sqrt{ \sqrt{ \sqrt{x} } } } = \sqrt[2.2.2.2]{x} = \sqrt[16]{x}$