Question

racionalize os denominadores​

Answer 1

A)

$\frac{15}{2 \sqrt{10} } = \frac{15}{2 \sqrt{10} } \times \frac{ \sqrt{10} }{ \sqrt{10} } = \frac{15 \sqrt{10} }{2 \sqrt{100} } \\ \frac{15 \sqrt{10} }{2 \times 10} = \frac{15 \sqrt{10} }{20} = \frac{3 \sqrt{10} }{4}$

B)

$\frac{8}{ \sqrt[4]{4} } = \frac{8}{ \sqrt[4]{4} } \times \frac{ \sqrt[4]{4} }{ \sqrt[4]{4} } = \frac{8 \sqrt[4]{4} }{ \sqrt[4]{16} } = \frac{8 \sqrt[4]{4} }{2} = 4 \sqrt[4]{4}$

C)

$\frac{1}{4 + \sqrt{2} } = \frac{1}{4 + \sqrt{2} } \times \frac{ \sqrt{2} }{ \sqrt{2} } = \frac{1 \sqrt{2} }{4 + \sqrt{4} } = \\ \frac{1 \sqrt{2} }{4 + 2} = \frac{1 \sqrt{2} }{6}$

D)

$\frac{ \sqrt{3} }{ \sqrt{3} - 1 } = \frac{ \sqrt{3} }{ \sqrt{3} - 1} \times \frac{ \sqrt{3} }{ \sqrt{3} } = \frac{ \sqrt{9} }{ \sqrt{9} - 1 } = \frac{3}{3 - 1} = \frac{3}{2}$

E)

$\frac{4 - 3 \sqrt{2} }{5 - \sqrt{2} } = \frac{4 - 3 \sqrt{2} }{5 - \sqrt{2} } \times \frac{ \sqrt{2} }{ \sqrt{2} } = \frac{4 - 3 \sqrt{4} }{5 - \sqrt{4} } = \\ \frac{4 - 3 \times 2}{5 - 2} = \frac{4 - 6}{3} = \frac{ - 2}{3}$