Question

OLHEM POR FAVOR E RESPONDAM

Resolva, aplicando as propriedades de radiciação.

1) $\sqrt[8]{9 ^{4} } =$  

2)$\sqrt[9]{ 4^{3} } =$

3)$\sqrt{9.16} =$

4) $\sqrt \frac{4}{9} =$

Answer 1

$1) \ \sqrt[8]{9^4}= \sqrt[8\div4]{9^{4\div4}}= \sqrt{9} \\ \\ 2) \ \sqrt[9]{4^3}= \sqrt[9\div3]{4^{3\div3}}= \sqrt[3]{4} \\ \\ 3) \ \sqrt{9.16}= \sqrt{9}. \sqrt{16}=4*4=12\\ \\ 4) \ \sqrt{\frac{4}{9}}=\frac{\sqrt4}{\sqrt9}=\frac{2}{3}$

Answer 2

1) $\sqrt[8]{9^4}=\sqrt[8]{(3^2)^4}=\sqrt[8]{3^8}=3$

2) $\sqrt[9]{4^3}=\sqrt[9]{(2^2)^3}=\sqrt[9]{2^6}=\sqrt[3]{2^2}=\sqrt[3]{4}$

3) $\sqrt{9}\cdot\sqrt{16}=\sqrt{9}\cdot\sqrt{16}=3\cdot4=12$

4) $\sqrt{\dfrac{4}{9}}=\dfrac{\sqrt{4}}{\sqrt{9}}=\dfrac{2}{3}$