▶️ Ejercicio 233 álgebra - Solucionario Baldor ✅✅

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CAPITULO XXXI

R a d i c a l e s
Simplificación de radicales

Ejercicio 233

Simplificar:

$\sqrt[4]{9} = \sqrt[4]{3^{2}} = 3^{\frac{2}{}} = 3^{\frac{1}{2}} = \sqrt{3}$
$\sqrt[6]{4} = \sqrt[6]{2^{2}} = 2^{\frac{2}{}} = 2^{\frac{1}{3}} = \sqrt[3]{2}$
$\sqrt[9]{27} = \sqrt[9]{3^{3}} = 3^{\frac{3}{}} = 3^{\frac{1}{3}} = \sqrt[3]{3}$
$\sqrt[8]{16} = \sqrt[8]{2^{4}} = 2^{\frac{4}{}} = 2^{\frac{1}{2}} = \sqrt{2}$
$3 \sqrt[12]{64} = 3 \sqrt[12]{2^{6}} = 3 (2^{\frac{6}{}}) = 3 (2^{\frac{1}{2}}) = 3 \sqrt{2}$
$\sqrt[4]{25 a^{2} b^{2}} = \sqrt[4]{5^{2} {(a b)}^{2}} = \sqrt[4]{{(5 a b)}^{2}} = {(5 a b)}^{\frac{2}{}} = {(5 a b)}^{\frac{1}{2}} = \sqrt{5 a b}$
$\begin{matrix} 5 \sqrt[6]{49 a^{2} b^{4}} & = 5 \sqrt[6]{7^{2} a^{2} b^{4}} \\ = 5 \sqrt[6]{{(7 a)}^{2} b^{4}} \\ = 5 {(7 a)}^{\frac{2}{}} b^{\frac{}{}} \\ = 5 {(7 a)}^{\frac{1}{3}} b^{\frac{2}{3}} \\ = 5 \sqrt[3]{7 a} . \sqrt[3]{b^{2}} \\ = 5 \sqrt[3]{7 a b^{2}} \end{matrix}$
$\sqrt[8]{81 x^{4} y^{8}} = \sqrt[8]{3^{4} x^{4} y^{8}} = \sqrt[8]{{(3 x)}^{4} y^{8}} = {(3 x)}^{\frac{4}{}} y^{\frac{8}{8}} = {(3 x)}^{\frac{1}{2}} y = y \sqrt{3 x}$
$\begin{matrix} \sqrt[10]{32 x^{10} y^{15}} & = \sqrt[10]{2^{5} x^{10} y^{15}} \\ = 2^{\frac{5}{}} x^{\frac{10}{10}} y^{\frac{}{}} \\ = 2^{\frac{1}{2}} x y^{\frac{3}{2}} \\ = \sqrt{2} x \sqrt{y^{3}} \\ = x \sqrt{2 y^{3}} \\ = x \sqrt{2 y^{2} y} \\ = x y \sqrt{2 y} \end{matrix}$
$\begin{matrix} \sqrt[12]{64 m^{6} n^{18}} & = \sqrt[12]{2^{6} m^{6} n^{18}} \\ = 2^{\frac{6}{}} m^{\frac{6}{}} n^{\frac{}{}} \\ = 2^{\frac{1}{2}} m^{\frac{1}{2}} n^{\frac{3}{2}} \\ = \sqrt{2} \sqrt{m} \sqrt{n^{3}} \\ = \sqrt{2 m} \sqrt{n^{2} n} \\ = n \sqrt{2 m} \sqrt{n} \\ = n \sqrt{2 m n} \end{matrix}$
$\begin{matrix} \sqrt[6]{343 a^{9} x^{12}} & = \sqrt[6]{343 a^{9} x^{12}} \\ = \sqrt[6]{7^{3} a^{9} x^{12}} \\ = 7^{\frac{3}{}} a^{\frac{}{}} x^{\frac{}{6}} \\ = 7^{\frac{1}{2}} a^{\frac{3}{2}} x^{2} \\ = \sqrt{7} \sqrt{a^{3}} x^{2} \\ = \sqrt{7} \sqrt{a^{2} a} x^{2} \\ = a \sqrt{7} \sqrt{a} x^{2} \\ = a x^{2} \sqrt{7 a} \end{matrix}$
$\begin{matrix} \sqrt[15]{m^{10} n^{15} x^{20}} & = m^{\frac{}{}} n^{\frac{15}{15}} x^{\frac{}{}} \\ = m^{\frac{2}{3}} n x^{\frac{4}{3}} \\ = \sqrt[3]{m^{2}} n \sqrt[3]{x^{4}} \\ = \sqrt[3]{m^{2}} n \sqrt[3]{x^{3} x} \\ = n x \sqrt[3]{m^{2}} \sqrt[3]{x} \\ = n x \sqrt[3]{m^{2} x} \end{matrix}$

Categories: Capítulo XXXI