$(sqrt(15)+sqrt3)^2-sqrt5(sqrt9+5sqrt2)-sqrt(50)(sqrt2-sqrt5)$

A cura di: Francesco Speciale

Svolgimento:
$(sqrt(15)+sqrt3)^2-sqrt5(sqrt9+5sqrt2)-sqrt(50)(sqrt2-sqrt5)=$
$=15+3+2sqrt(45)-sqrt5(3+5sqrt2)-5sqrt2(sqrt2-sqrt5)=$
$=15+3+6sqrt5-3sqrt5-5sqrt(10)-10+5sqrt(10)$
Semplificando si ha che
$=15+3+6sqrt5-3sqrt5-5sqrt(10)-10+5sqrt(10)=8+3sqrt5$.