Explicație pas cu pas:[tex]\sqrt{3}\cdot \left(4\sqrt{2}+5\sqrt{3}\right)+4\sqrt{6}\cdot \left(\sqrt{6}-1\right) = \sqrt{3}\cdot4\sqrt{2} + \sqrt{3} \cdot 5\sqrt{3} + 4\sqrt{6} \cdot \sqrt{6} - 4\sqrt{6} = 4 \cdot \sqrt{3 \cdot 2} + 5\sqrt{3 \cdot 3} + 4\sqrt{6 \cdot 6} - 4\sqrt{6} = 4\sqrt{6} + 5 \cdot 3 + 4 \cdot 6 - 4\sqrt{6} = 5 \cdot 3+ 4 \cdot 6= 15 + 24 = 39[/tex]
[tex]\frac{6}{\sqrt{3} } - \frac{8}{\sqrt{12} } + \frac{9}{\sqrt{27} } = \frac{6}{\sqrt{3} } - \frac{8}{2\sqrt{3} } + \frac{9}{3\sqrt{3} } = \frac{\sqrt{3} \cdot 6}{\sqrt{3} \cdot \sqrt{3} } - \frac{\sqrt{3} \cdot 8}{2 \cdot \sqrt{3} \cdot \sqrt{3} } + \frac{\sqrt{3} \cdot 9}{\sqrt{3} \cdot 3\sqrt{3} } = \frac{6\sqrt{3} }{3} - \frac{8\sqrt{3} }{2 \cdot 3} + \frac{9\sqrt{3} }{3 \cdot 3} = \frac{6\sqrt{3} }{3} - \frac{8\sqrt{3} }{6} + \frac{9\sqrt{3} }{9} =[/tex]
[tex]\frac{6 \cdot 6\sqrt{3} }{6 \cdot 3} - \frac{3 \cdot 8\sqrt{3} }{3 \cdot 6} + \frac{2 \cdot 9\sqrt{3} }{2 \cdot 9} = \frac{36\sqrt{3} }{18} - \frac{24\sqrt{3} }{18} + \frac{18\sqrt{3} }{18} = \frac{12\sqrt{3} }{18} + \frac{18\sqrt{3} }{18} = \frac{30\sqrt{3} }{18} = \frac{5\sqrt{3} }{3}[/tex]
