1.
[tex]\it a=3\sqrt{48}-2\sqrt{108}=3\sqrt{16\cdot3}-2\sqrt{36\cdot3}=12\sqrt3-12\sqrt3=0\\ \\ a\cdot b=0\cdotb=0,\ pentru \ \ oricare \ b\in\mathbb{R}[/tex]
2.
[tex]\it a=2\sqrt{216}-6\sqrt{96}+5\sqrt{54}-3\sqrt{150}+\sqrt{600}=\\ \\ =\sqrt6(2\sqrt{36}-6\sqrt{16}+5\sqrt{9}-3\sqrt{25}+\sqrt{100})=\sqrt6(12-24+15-15+10)=\\ \\ =\sqrt6\cdot(-2)=-2\sqrt6[/tex]
3.
[tex]\it (2\sqrt{10}-\sqrt7+\sqrt5)(2\sqrt{10}+\sqrt7+\sqrt5)=40+2\sqrt{70}+2\sqrt{50}-2\sqrt{70}-7-\\ \\ -\sqrt{35}+2\sqrt{50}+\sqrt{35}+5=38-4\sqrt{50}=38-4\sqrt{25\cdot2}=38-20\sqrt2[/tex]
4.
[tex]\it A=(8\sqrt3+14\sqrt3-12\sqrt3):\sqrt{75}=(10\sqrt3):(5\sqrt3)=2\in\mathbb{N}[/tex]
