Ejercicio 234

octubre 30, 2019abril 14, 2019 por Gestor Baldor

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CAPITULO XXXI

R a d i c a l e s
Introducción de cantidades bajo el signo radical

Ejercicio 234

Hacer enteros a los radicales:

$2 \sqrt{3} = \sqrt{2^{2} .3} = \sqrt{4.3} = \sqrt{12}$
$3 \sqrt{5} = \sqrt{3^{2} .5} = \sqrt{9.5} = \sqrt{45}$
$5 a \sqrt{b} = \sqrt{{(5 a)}^{2} b} = \sqrt{25 a^{2} b}$
$\frac{1}{2} \sqrt{2} = \sqrt{\frac{1}{2^{2}} 2} = \sqrt{\frac{1}{2}}$
$3 a \sqrt{2 a^{2}} = \sqrt{{(3 a)}^{2} 2 a^{2}} = \sqrt{3^{2} a^{2} 2 a^{2}} = \sqrt{9.2 a^{4}} = \sqrt{18 a^{4}}$
$5 x^{2} y \sqrt{3} = \sqrt{3 {(5 x^{2} y)}^{2}} = \sqrt{3. 5^{2} x^{4} y^{2}} = \sqrt{75 x^{4} y^{2}}$
$a b^{2} \sqrt[3]{a^{2} b} = \sqrt[3]{{(a b^{2})}^{2} a^{2} b} = \sqrt[3]{a^{2} b^{4} a^{2} b} = \sqrt[3]{a^{4} b^{5}}$
$4 m \sqrt[3]{2 m^{2}} = \sqrt[3]{2 m^{2} {(4 m)}^{2}} = \sqrt[3]{2 m^{2} 4^{2} m^{2}} = \sqrt[3]{2 m^{2} 16 m^{2}} = \sqrt[3]{32 m^{4}}$
$2 a \sqrt[4]{8 a b^{3}} = \sqrt[4]{8 a b^{3} {(2 a)}^{2}} = \sqrt[4]{8 a b^{3} 2^{2} a^{2}} = \sqrt[4]{8 a b^{3} 4 a^{2}} = \sqrt[4]{32 a^{3} b^{3}}$
$(a + b) \sqrt{\frac{a}{a + b}} = \sqrt{\frac{a}{a + b} {(a + b)}^{2}} = \sqrt{a (a + b)} = \sqrt{a^{2} + a b}$
$(x + 1) \sqrt{\frac{2 x}{x + 1}} = \sqrt{\frac{2 x}{x + 1} {(x + 1)}^{2}} = \sqrt{2 x (x + 1)} = \sqrt{2 x^{2} + 2 x}$
$(x - 1) \sqrt{\frac{x - 2}{x - 1}} = \sqrt{\frac{x - 2}{x - 1} {(x - 1)}^{2}} = \sqrt{(x - 2) (x - 1)} = \sqrt{x^{2} - 3 x + 2}$