Question

ayuda con esto porfis❤​

Answer 1

Respuesta:

$\boxed{begin}{matrix}a).=\sqrt{3}&b).=-4\pi\sqrt{2}\\\\c).=\frac{\sqrt{14}}{14}&d).=\frac{\sqrt{5}}{55}\\e).=\frac{2\sqrt{65}}{13}\end{matrix}}$

Explicación paso a paso:

$\textbf{Racionaliza las siguientes expresiones}$

$\frac{3}{\sqrt{3}}$

$\textbf{Para racionalizar,habr\'a que multiplicar por el denominador}\\\textbf{a toda la expresi\'on (amplificar),entonces:}$

$a).\\\left(\frac{\sqrt{3}}{\sqrt{3}}\right)\left(\frac{3}{\sqrt{3}}\right)=\frac{3\sqrt{3}}{(\sqrt{3})^{2}}=\frac{3\sqrt{3}}{3}=\\\\=\sqrt{3}$

$b).\\-\frac{8\pi}{\sqrt{2}}\\\\\left(\frac{\sqrt{2}}{\sqrt{2}}\right)\left(-\frac{8\pi}{\sqrt{2}}\right)=\frac{-8\pi\sqrt{2}}{(\sqrt{2})^{2}}=\\\\=\frac{-8\pi\sqrt{2}}{2}=-4\pi\sqrt{2}$

$c).\\\frac{2}{\sqrt{28}}\\\\\left(\frac{\sqrt{28}}{\sqrt{28}}\right)\left(\frac{\sqrt{2}}{\sqrt{28}}\right)=\frac{\sqrt{2}\sqrt{28}}{(\sqrt{28})^{2}}=\\\\=\frac{\sqrt{2}\sqrt{28}}{28}=\frac{\sqrt{(2)(28)}}{28}=\\\\=\frac{\sqrt{56}}{28}=\frac{\sqrt{(4)(14)}}{28}=\\\\=\frac{\sqrt{4}\sqrt{14}}{28}=\frac{2\sqrt{14}}{28}=\frac{\sqrt{14}}{14}$

$d).-\\\frac{1}{11\sqrt{5}}\\\\\left(\frac{11\sqrt{5}}{11\sqrt{5}}\right)\left(\frac{1}{11\sqrt{5}}\right)=\frac{11\sqrt{5}}{(11\sqrt{5})^{2}}=\\\\=\frac{11\sqrt{5}}{(11)^{2}(\sqrt{5})^{2}}=\frac{11\sqrt{5}}{121*5}=\\\\=\frac{11\sqrt{5}}{605}=\frac{\sqrt{5}}{55}$

$e).\\\frac{4\sqrt{5}}{2\sqrt{13}}\\\\\left(\frac{2\sqrt{13}}{2\sqrt{13}}\right)\left(\frac{4\sqrt{5}}{2\sqrt{13}}\right)=\frac{(2)(4)\sqrt{13}\sqrt{5}}{(2)^{2}(\sqrt{13})^{2}}=\frac{8\sqrt{5}\sqrt{13}}{4*(13)}=\\\\=\frac{8\sqrt{(5)(13)}}{52}=\frac{8\sqrt{65}}{52}=\frac{2\sqrt{65}}{13}$