Ejercicio 243

octubre 30, 2019abril 14, 2019 por Gestor Baldor

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CAPITULO XXXI

R a d i c a l e s
División de radicales del mismo índice

Ejercicio 243

Dividir:

$\begin{matrix} 4 \sqrt{6} \div 2 \sqrt{3} \\ 4 \sqrt{6} \div 2 \sqrt{3} & = \frac{}{2} \sqrt{\frac{}{3}} \\ = 2 \sqrt{2} \end{matrix}$
$\begin{matrix} 2 \sqrt{3 a} \div 10 \sqrt{a} \\ 2 \sqrt{3 a} \div 10 \sqrt{a} & = \frac{2}{} \sqrt{\frac{3 a}{a}} \\ = \frac{1}{5} \sqrt{3} \end{matrix}$
$\begin{matrix} \frac{1}{2} \sqrt{3 x y} \div \frac{3}{4} \sqrt{x} \\ \frac{1}{2} \sqrt{3 x y} \div \frac{3}{4} \sqrt{x} & = \frac{\frac{1}{2}}{\frac{3}{}} \sqrt{\frac{3 x y}{x}} \\ = \frac{2}{3} \sqrt{3 y} \end{matrix}$
$\begin{matrix} \sqrt{75 x^{2} y^{3}} \div 5 \sqrt{3 x y} \\ \sqrt{75 x^{2} y^{3}} \div 5 \sqrt{3 x y} & = \frac{1}{5} \sqrt{\frac{x^{2} y^{}}{3 x y}} \\ = \frac{1}{5} \sqrt{25 x y^{2}} \\ = \frac{1}{5} 5 y \sqrt{x} \\ = y \sqrt{x} \end{matrix}$
$\begin{matrix} 3 \sqrt[3]{16 a^{5}} \div 4 \sqrt[3]{2 a^{2}} \\ 3 \sqrt[3]{16 a^{5}} \div 4 \sqrt[3]{2 a^{2}} & = \frac{3}{4} \sqrt[3]{\frac{a^{}}{2 a^{2}}} \\ = \frac{3}{4} \sqrt[3]{8 a^{3}} \\ = \frac{3}{} 2 a \\ = \frac{3}{2} a \end{matrix}$
$\begin{matrix} \frac{5}{6} \sqrt{\frac{1}{2}} \div \frac{10}{3} \sqrt{\frac{2}{3}} \\ \frac{5}{6} \sqrt{\frac{1}{2}} \div \frac{10}{3} \sqrt{\frac{2}{3}} & = \frac{\frac{5}{}}{\frac{}{3}} \sqrt{\frac{\frac{1}{2}}{\frac{2}{3}}} \\ = \frac{1}{4} \sqrt{\frac{3}{4}} \\ = \frac{1}{4} \sqrt{\frac{3}{2^{2}}} \\ = \frac{1}{8} \sqrt{3} \end{matrix}$
$\begin{matrix} 4 x \sqrt{a^{3} x^{2}} \div 2 \sqrt{a^{2} x^{3}} \\ 4 x \sqrt{a^{3} x^{2}} \div 2 \sqrt{a^{2} x^{3}} & = \frac{}{2} x \sqrt{\frac{a^{3} x^{2}}{a^{2} x^{3}}} \\ = 2 x \sqrt{\frac{a}{x}} \\ = 2 x \sqrt{\frac{a}{x} \times \frac{x}{x}} \\ = 2 x \sqrt{\frac{a x}{x^{2}}} \\ = 2 \frac{x}{x} \sqrt{a x} \\ = 2 \sqrt{a x} \end{matrix}$
$\begin{matrix} \frac{2 a}{3} \sqrt[3]{x^{2}} \div \frac{a}{3 x^{2}} \sqrt[3]{x^{3}} \\ \frac{2 a}{3} \sqrt[3]{x^{2}} \div \frac{a}{3 x^{2}} \sqrt[3]{x^{3}} & = \frac{\frac{2 a}{3}}{\frac{a}{3 x^{2}}} \sqrt[3]{\frac{x^{2}}{x^{3}}} \\ = 2 x^{2} \sqrt[3]{\frac{1}{x}} \\ = 2 x^{2} \sqrt[3]{\frac{1}{x} \times \frac{x^{2}}{x^{2}}} \\ = 2 x^{2} \sqrt[3]{\frac{x^{2}}{x^{3}}} \\ = 2 \frac{x^{2}}{x} \sqrt[3]{x^{2}} \\ = 2 x \sqrt[3]{x^{2}} \end{matrix}$
$\begin{matrix} \frac{1}{3} \sqrt[3]{\frac{1}{2}} \div \frac{1}{6} \sqrt[3]{\frac{1}{3}} \\ \frac{1}{3} \sqrt[3]{\frac{1}{2}} \div \frac{1}{6} \sqrt[3]{\frac{1}{3}} & = \frac{\frac{1}{3}}{\frac{1}{}} \sqrt[3]{\frac{\frac{1}{2}}{\frac{1}{3}}} \\ = 2 \sqrt[3]{\frac{3}{2}} \\ = 2 \sqrt[3]{\frac{3}{2} \times \frac{2^{2}}{2^{2}}} \\ = 2 \sqrt[3]{\frac{12}{2^{3}}} \\ = \frac{2}{2} \sqrt[3]{12} \\ = \sqrt[3]{12} \end{matrix}$