Question

Resuelva las siguientes operaciones con radicales semejantes

Answer 1

Las operaciones con radicales semejantes se realizan sobre los números que los multiplican, los cuales se consideran coeficientes numeradores de estos radicales.

Explicación paso a paso:

$\bold{5.\quad\frac{20}{13}\sqrt[3]{5}~+~\frac{9}{13}\sqrt[3]{5}~+~\frac{10}{13}\sqrt[3]{5}}$

$\frac{20}{13}\sqrt[3]{5}~+~\frac{9}{13}\sqrt[3]{5}~+~\frac{10}{13}\sqrt[3]{5}~=~[\frac{20}{13}~+~\frac{9}{13}~+~\frac{10}{13}]\sqrt[3]{5}~=~\bold{3\sqrt[3]{5}}$

$\bold{6.\quad\frac{2}{7}\sqrt[3]{5}~-~\frac{1}{13}\sqrt[3]{5}}$

$\frac{2}{7}\sqrt[3]{5}~-~\frac{1}{13}\sqrt[3]{5}~=~[\frac{2}{7}~-~\frac{1}{13}]\sqrt[3]{5}~=~\bold{\frac{19}{91}\sqrt[3]{5}}$

$\bold{7.\quad3\sqrt[2]{7}~+~12\sqrt[2]{7}~+~2\sqrt[3]{2}~-~10\sqrt[3]{2}}$

$3\sqrt[2]{7}~+~12\sqrt[2]{7}~+~2\sqrt[3]{2}~-~10\sqrt[3]{2}~=~[3~+~12]\sqrt[2]{7}~+~[2~-~10]\sqrt[3]{2}~=~\bold{15\sqrt[2]{7}~-~8\sqrt[3]{2}}$

$\bold{8.\quad\frac{2}{13}\sqrt[3]{\frac{5}{7}}~\cdot~\frac{9}{7}\sqrt[3]{\frac{9}{13}}}$

$\frac{2}{13}\sqrt[3]{\frac{5}{7}}\cdot\frac{9}{7}\sqrt[3]{\frac{9}{13}}~=~(\frac{2}{13})\cdot(\frac{9}{7})\sqrt[3]{\frac{5}{7}}\sqrt[3]{\frac{9}{13}}~=~(\frac{2\cdot9}{13\cdot7})\sqrt[3]{\frac{5\cdot9}{7\cdot13}}~=~\bold{\frac{18}{91}\sqrt[3]{\frac{45}{91}}}$

$\bold{9.\quad\frac{2}{7}\div\frac{3}{13}\sqrt[3]{\frac{12}{25}\div\frac{9}{13}}}$

$\frac{2}{7}\div\frac{3}{13}\sqrt[3]{\frac{12}{25}\div\frac{9}{13}}~=~\frac{\frac{2}{7}}{\frac{3}{13}}\sqrt[3]{\frac{\frac{12}{25}}{\frac{9}{13}}}~=~\frac{(2)\cdot(13)}{(3)\cdot(7)}\sqrt[3]{\frac{(12)\cdot(13)}{(25)\cdor(9)}}~=~\bold{\frac{26}{21}\sqrt[3]{\frac{52}{75}}}$