Question

resolver las siguientes sumas y restas de radicales

Answer 1

Respuesta:

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Explicación paso a paso:

$\frac{1}{2}\sqrt{2}-5\sqrt{2}\\\\\mathrm{Factorizar\:el\:termino\:comun\:}\sqrt{2}\\\\=\sqrt{2}\left(\frac{1}{2}-5\right)\\\\=-\sqrt{2}\frac{9}{2}\\\\\mathrm{Multiplicar\:fracciones}:\quad \:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}\\\\=-\frac{9\sqrt{2}}{2}\\\\\mathrm{Aplicar\:las\:leyes\:de\:los\:exponentes}:\quad \sqrt[n]{a}=a^{\frac{1}{n}}\\\\=\frac{9\cdot \:2^{\frac{1}{2}}}{2}\\\\\mathrm{Aplicar\:las\:leyes\:de\:los\:exponentes}:\quad \frac{x^a}{x^b}=\frac{1}{x^{b-a}}$

$=\frac{9}{2^{1-\frac{1}{2}}}\\\\=\frac{9}{2^{\frac{1}{2}}}\\\\\mathrm{Aplicar\:las\:leyes\:de\:los\:exponentes}:\quad \:a^{\frac{1}{n}}=\sqrt[n]{a}\\\\=-\frac{9}{\sqrt{2}}\\\\\mathrm{Racionalizar\:}-\frac{9}{\sqrt{2}}:\quad -\frac{9\sqrt{2}}{2}\\\\=-\frac{9\sqrt{2}}{2}$

$2\sqrt{3}+3\sqrt{3}\\\\=5\sqrt{3}$

$-\frac{3}{4}\sqrt[5]{6}+3\sqrt[5]{6}+4\sqrt[5]{6}\\\\\mathrm{Factorizar\:el\:termino\:comun\:}\sqrt[5]{6}\\\\=\sqrt[5]{6}\left(-\frac{3}{4}+3+4\right)\\\\=\sqrt[5]{6}\frac{25}{4}\\\\\mathrm{Multiplicar\:fracciones}:\quad \:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}\\\\=\frac{25\sqrt[5]{6}}{4}\\\mathrm{Factorizar}\:\sqrt[5]{6}:\quad \sqrt[5]{2}\sqrt[5]{3}\\\\\mathrm{Factorizar}\:4:\quad 2^2\\\\=\frac{25\sqrt[5]{2}\sqrt[5]{3}}{2^2}\\\\\mathrm{Cancelar\:}\frac{25\sqrt[5]{2}\sqrt[5]{3}}{2^2}$

$=\frac{25\sqrt[5]{3}}{2^{\frac{9}{5}}}\\\\=\frac{25\sqrt[5]{3}}{2\cdot \:2^{\frac{4}{5}}}\\\\\mathrm{Racionalizar\:}\frac{25\sqrt[5]{3}}{2\cdot \:2^{\frac{4}{5}}}:\quad \frac{25\sqrt[5]{2}\sqrt[5]{3}}{4}\\\\=\frac{25\sqrt[5]{2}\sqrt[5]{3}}{4}$

$-5\sqrt[4]{4}-3\sqrt[7]{4}+10\sqrt[7]{4}-9\sqrt[7]{4}\\\\\mathrm{Sumar\:elementos\:similares:}\:-3\sqrt[7]{4}+10\sqrt[7]{4}-9\sqrt[7]{4}=-2\sqrt[7]{4}\\\\=-5\sqrt[4]{4}-2\sqrt[7]{4}\\\\=-5\sqrt{2}-2\sqrt[7]{4}$

$-\sqrt[4]{8}+2\sqrt[4]{8}+4\sqrt[4]{8}\\\\\mathrm{Sumar\:elementos\:similares:}\:-\sqrt[4]{8}+2\sqrt[4]{8}+4\sqrt[4]{8}=5\sqrt[4]{8}\\\\=5\sqrt[4]{8}$