esegui le operazioni
[math]root(3)((x^2y+xy^2)/(4x^3)) \cdot root(4)((x^2+y^2-2xy)/(x^2+y^2+2xy)):root(6)((x-y)^3/(4x^3))=[/math]
[math]root(3)((x^2y+xy^2)/(4x^3)) \cdot root(4)((x^2+y^2-2xy)/(x^2+y^2+2xy)):root(6)((x-y)^3/(4x^3))=[/math]
[math]=root(3)((xy(x+y))/(4x^3)) \cdot \sqrt{(x-y)/(x+y)} \cdot root(6)((4x^3)/(x-y)^3)=[/math]
Il m.c.m. degli indici
[math]6[/math]
[math]root(6)((x^2y^2(x+y)^2)/(16x^6) \cdot (x-y)^3/(x+y)^3 \cdot (4x^3)/(x-y)^3[/math]
Semplificando opportunamente i fattori del numeratore con quelli del denominatore si ha
[math]root(6)(y^2/(4x(x+y)))[/math]
.
![Radicali: [math] {\sqrt[{{3}}]{{\frac{{{x}^{3}+{y}^{3}}}{{{x}^{2}+{y}^{2}}}}}}:{\sqrt[{{4}}]{{\frac{{{x}^{2}-{x}{y}+{y}^{2}}}{{{x}^{4}-{y}^{4}}}}}} [/math]](https://cdn.skuola.net/shared/thumb/159x141/news_foto/images/stories/esercizi/rad-2114.jpg)
