Question

8. Aplicando as propriedades de raizes, encontre o valor de cada expressão:

$\sqrt{ 3^{2} } = \sqrt[10]{32} = \sqrt[15]{ 3^{5} }= \sqrt[3]{ 12^{3} }= \sqrt[5]{ \sqrt[3]{3} }= \sqrt{ \sqrt{16} }= \sqrt{3*12}= \sqrt[3]{8*125}= \sqrt[2]{ \frac{81}{25} }= \sqrt{ \frac{1}{8} } =$

Answer 1

$\sqrt{3^2}= \sqrt{9}=3$

$\sqrt[10]{32} = \sqrt[10]{2^5}=2^\frac{5}{10}= 2^\frac{1}{2}= \sqrt{2}$

$\sqrt[15]{3^5}=3^ \frac{5}{15} =3^ \frac{1}{3} = \sqrt[3]{3}$

$\sqrt[3]{12^3}=12$

$\sqrt[5]{ \sqrt[3]{3} } = \sqrt[5]{3^ \frac{1}{3} } =3^(\frac{1}{3}.\frac{1}{5})=3^ \frac{1}{15} = \sqrt[15]{3}$

$\sqrt{ \sqrt{16} } = \sqrt{4} =2$

$\sqrt{3.12}= \sqrt{36} =8$

$\sqrt[3]{8.125} = \sqrt[3]{8} . \sqrt[3]{125} =2.5=10$

$\sqrt{ \frac{81}{25} }= \frac{9}{5}$

$\sqrt{ \frac{1}{9} } = \frac{ \sqrt{1} }{ \sqrt{9} } = \frac{1}{3}$