Question

Transforme em uma unica raiz

Answer 1

a)
$\frac{ \sqrt{12} \times \sqrt{15} }{ \sqrt{8} } = \\ \frac{ \sqrt{12 \times 15} }{ \sqrt{8} } = \\ \sqrt{ \frac{12 \times 15}{8} } = \\ \sqrt{ \frac{180}{8} } = \\ \sqrt{ \frac{45}{4} }$
b)
$\frac{ \sqrt[3]{9} \times \sqrt[3]{10} }{ \sqrt[3]{12} \times \sqrt[3]{15} } = \\ \frac{ \sqrt[3]{9 \times 10} }{ \sqrt[3]{12 \times 15} } = \\ \sqrt[3]{ \frac{90}{180} } = \\ \sqrt[3]{ \frac{1}{2} }$

c)
$\frac{ \sqrt[6]{4} \times \sqrt{ \sqrt[3]{10} } }{ \sqrt[6]{120} } = \\ \frac{ \sqrt[6]{4} \times \sqrt[6]{10} }{ \sqrt[6]{120} } = \\ \frac{ \sqrt[6]{4 \times 10} }{ \sqrt[6]{120} } = \\ \frac{ \sqrt[6]{40} }{ \sqrt[6]{120} } = \\ \sqrt[6]{ \frac{40}{120} } = \\ \sqrt[6]{ \frac{1}{3} }$
d)
$\frac{ \sqrt[8]{14} \times \sqrt[4]{\sqrt{10} } }{ \sqrt{ \sqrt{ \sqrt{2} } } } = \\ \frac{ \sqrt[8]{14} \times \sqrt[8]{10} }{ \sqrt[8]{2} } = \\ \frac{ \sqrt[8]{14 \times 10} }{ \sqrt[8]{2} } = \\ \frac{ \sqrt[8]{140} }{ \sqrt[8]{2} } = \\ \sqrt[8]{ \frac{140}{2} } = \\ \sqrt[8]{70}$