Question

racionaliza √2/√7 , √5+√3/√5-√3 , √2/√3n^3-√4m^2

Answer 1

Respuesta:

Explicación paso a paso:

a)

$\frac{\sqrt{2} }{\sqrt{7} }.\frac{\sqrt{7}}{\sqrt{7}}= \frac{\sqrt{2.7}}{\sqrt{7^{2} }}=\frac{\sqrt{14}}{7}$

b)

$\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}=\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}.\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}+\sqrt{3}}=\frac{(\sqrt{5}+\sqrt{3})^{2} }{5-3}=\frac{5+2\sqrt{15}+3}{2}=\frac{8+2\sqrt{15}}{2}=\frac{2(4+\sqrt{15})}{2}=4+\sqrt{15}$

c)

$\frac{\sqrt{2}}{\sqrt{3n^{3} }-\sqrt{4m^{2}} }=\frac{\sqrt{2}}{n\sqrt{3n}-2m}=\frac{\sqrt{2}}{n\sqrt{3n}-2m}.\frac{n\sqrt{3n}+2m}{n\sqrt{3n}+2m}=\frac{\sqrt{6n}n+2\sqrt{2}m}{3n^{3}-4m^{2} }$