Question

Como transformar em um único radical?

 

 Quero saber como que se chega a esses resultados:

 

a)  (√12×√15)/(√8) =   o resultado é (3√10)/2

 

b) ∛9×∛10)/(∛12×∛15) = o resultado é (∛4)/2

Answer 1

a)

 

$\frac{\sqrt{12} \times \sqrt{15}}{\sqrt{8}} = \\\\ \frac{\sqrt{2^2 \times 3} \times \sqrt{3 \times 5}}{\sqrt{2^3}} = \\\\ \frac{\sqrt{2^2 \times 3^2 \times 5}}{\sqrt{2^2 \times 2}} = \\\\ \frac{2 \times 3\sqrt{5}}{2\sqrt{2}} = \\\\ \frac{3\sqrt{5}}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \\\\ \boxed{\frac{3\sqrt{10}}{2}}$

 

 

b)

 

$\frac{\sqrt[3]{9} \times \sqrt[3]{10}}{\sqrt[3]{12} \times \sqrt[3]{15}} \Rightarrow \frac{\sqrt[3]{3^2} \times \sqrt[3]{2 \times 5}}{\sqrt[3]{2^2 \times 3} \times \sqrt[3]{3 \times 5}} \Rightarrow \frac{\sqrt[3]{2 \times 3^2 \times 5}}{\sqrt[3]{2^2 \times 3^2 \times 5}} =$

 

$\sqrt[3]{\frac{2 \times 3^2 \times 5}{2^2 \times 3^2 \times 5}} \Rightarrow \sqrt[3]{\frac{1}{2}} \Rightarrow \frac{1}{\sqrt[3]{2}} \Rightarrow \frac{1}{\sqrt[3]{2}} \times \frac{\sqrt[3]{2^2}}{\sqrt[3]{2^2}} = \\\\\\ \frac{\sqrt[3]{4}}{\sqrt[3]{2^3}} \Rightarrow \boxed{\frac{\sqrt[3]{4}}{2}}$