Question

Simplifique as expressões .
a) 2 raiz de 5 (3 + raiz de 5 ) =
b) 3 raiz de 2 ( 2 raiz de 3 - raiz de 2 ) =
c) ( 2 - raiz de 3 ) ( 1 + raiz de 2 ) = 
d) ( raiz de 3 + 1 ) ( raiz de 3 -1 ) =
e) ( 2 raiz de 2 -3) (2 raiz de 2 + 3) =
f) (2+ raiz de 3 ) ao quadrado =
g) ( raiz de 3 -1 ) ao quadrado =

Answer 1

$a) 2 \sqrt{5}(3+ \sqrt{5})=6\sqrt5+10 \\ b) 3\sqrt2(2\sqrt3- \sqrt{2}=6\sqrt6-6 \\ c) (2-\sqrt3)(1+\sqrt2)= 2+2\sqrt2-\sqrt3-\sqrt6 \\ d)(\sqrt3+1)(\sqrt3-1)=(\sqrt3)^2-1^2=3-1=2 \\ e)(2\sqrt2-3)(2\sqrt2+3)=(2\sqrt2)^2-3^2=8-9=-1 \\ f)(2+\sqrt3)^2=4+4\sqrt3+(\sqrt3)^2=4+4\sqrt3+3=7+4\sqrt3 \\ g)\sqrt3-1)^2=(\sqrt3)^2-2\sqrt3+1=3-2\sqrt3+1=4-2\sqrt3$