Question

racionalize os denominadores das frações a seguir ​

Answer 1

a)

$\frac{3}{\sqrt{6}}~.~\frac{\sqrt{6}}{\sqrt{6}}~=~\frac{3~.~\sqrt{6}}{\sqrt{6}^2}~=~\frac{3\sqrt{6}}{6}~=~\boxed{\frac{\sqrt{3}}{2}}$

b)

$\frac{8}{\sqrt{3}}~.~\frac{\sqrt{3}}{\sqrt{3}}~=~\frac{8~.~\sqrt{3}}{\sqrt{3}^2}~=~\boxed{\frac{8\sqrt{3}}{3}}$

c)

$\frac{5\sqrt{2}}{\sqrt{6}}~.~\frac{\sqrt{6}}{\sqrt{6}}~=~\frac{5\sqrt{2}~.~\sqrt{6}}{\sqrt{6}^2}~=~\frac{5\sqrt{2~.~6}}{6}~=~\boxed{\frac{5\sqrt{12}}{6}}$

Answer 2

a)

$\frac{3}{ \sqrt{6} } = \frac{3 \sqrt{6} }{6 } = \frac{ \sqrt{6} }{2}$

b)

$\frac{5 \sqrt{2} }{ \sqrt{6} } = \frac{5 \sqrt{2}. \sqrt{6} }{6} = \frac{10 \sqrt{3} }{6} = \frac{5 \sqrt{3} }{3}$