Question

64. racionalize os denominadores ​

Answer 1

a)

$\frac{4}{\sqrt{15}}~.~\frac{\sqrt{15}}{\sqrt{15}}~=\\\\\\=~\frac{4~.~\sqrt{15}}{\sqrt{15}^{\,2}}\\\\\\=~\boxed{\frac{4\sqrt{15}}{15}}$

b)

$\frac{9}{\sqrt{6}}~.~\frac{\sqrt{6}}{\sqrt{6}}~=\\\\\\=~\frac{9~.~\sqrt{6}}{\sqrt{6}^{\,2}}\\\\\\=~\frac{9\sqrt{6}}{6}\\\\\\=~\boxed{\frac{3\sqrt{6}}{2}}$

c)

$\frac{6}{5\sqrt{22}}~.~\frac{\sqrt{22}}{\sqrt{22}}~=\\\\\\=~\frac{6~.~\sqrt{22}}{5\sqrt{22}^{\,2}}\\\\\\=~\frac{6\sqrt{22}}{5~.~22}\\\\\\=~\frac{6\sqrt{22}}{110}\\\\\\=~\boxed{\frac{3\sqrt{22}}{55}}$

d)

$\frac{8}{10+\sqrt{3}}~.~\frac{10-\sqrt{3}}{10-\sqrt{3}}~=\\\\\\=~\frac{8~.~10~-~8~.~\sqrt{3}}{10^2~-~10~.~\sqrt{3}~+~10~.~\sqrt{3}~-~\sqrt{3}^{\,2}}\\\\\\=~\frac{80-8\sqrt{3}}{100~-~10\sqrt{3}~+~10\sqrt{3}~-~3}\\\\\\=~\boxed{\frac{80-8\sqrt{3}}{97}}$