Question

Simplifica los siguientes radicales.

Answer 1

Hola!

Explicación paso a paso:

■》Solución "a":

$\frac{3}{2} \sqrt[3]{8 {x}^{3} {y}^{3} } \\ \\ = \frac{3}{2} \sqrt[3]{ {2}^{3} {x}^{3} {y}^{3} } \\ \\ = \frac{3}{2} \sqrt[3]{ {(2xy)}^{3} } \\ \\ = \frac{3}{2} {(2xy)}^{ \frac{3}{3} } \\ \\ = \frac{3}{2} {(2xy)}^{1} \\ \\ = \frac{3}{2} (2xy) \\ \\ = 3xy$

■》Solución "b":

$\sqrt[4]{32 {a}^{9} {b}^{4} } \\ = \sqrt[4]{ {2}^{5} {a}^{9} {b}^{4} } \\ = \sqrt[4]{ {2}^{4} {a}^{4} {b}^{4} (2 {a}^{5} )} \\ = \sqrt[4]{ {(2ab)}^{4}(2 {a}^{5} ) } \\ = \sqrt[4]{ {2ab}^{4} } . \sqrt[4]{(2 {a}^{5})} \\ = 2ab \sqrt[4]{2 {a}^{5} }$