Răspuns:
3.
a) [tex]6\sqrt{3}[/tex]
b) [tex]-2\sqrt{2}[/tex]
c) [tex]-3\sqrt{2} - 6\sqrt{3}[/tex]
d) [tex]9\sqrt{5} - 6\sqrt{3}[/tex]
4.
a) [tex]2\sqrt{2}[/tex]
b) [tex]-\sqrt{2}[/tex]
c) [tex]-\sqrt{3}[/tex]
d) [tex]\sqrt{6}[/tex]
Explicație pas cu pas:
3.
a) [tex]\sqrt{27} -\sqrt{12} + \sqrt{75} = \sqrt{9*3} - \sqrt{4*3} + \sqrt{25*3} = 3\sqrt{3} - 2\sqrt{3} + 5\sqrt{3} = 6\sqrt{3}[/tex]
b) [tex]10\sqrt{8} -4\sqrt{18} -2\sqrt{50} = 10\sqrt{4*2} - 4\sqrt{9*2} - 2\sqrt{25*2} = 20\sqrt{2} - 12\sqrt{2} - 10\sqrt{2} = -2\sqrt{2}[/tex]
c) [tex]\sqrt{8} -\sqrt{50} - \sqrt{300} +\sqrt{48} = 2\sqrt{2} - 5\sqrt{2} - 10\sqrt{3} + 4\sqrt{3} = -3\sqrt{2} - 6\sqrt{3}[/tex]
d) [tex]3\sqrt{20} -4\sqrt{27} + \sqrt{45} +3\sqrt{12} = 3\sqrt{4*5} -4\sqrt{9*3} +\sqrt{9*5} +3\sqrt{4*3} = 6\sqrt{5} -12\sqrt{3} +3\sqrt{5} +6\sqrt{3} = 9\sqrt{5} -6\sqrt{3}[/tex]
4.
a) [tex]\sqrt{2} + \sqrt{28} : \sqrt{14} = \sqrt{2} + \sqrt{\frac{28}{14} } = \sqrt{2} + \sqrt{2} = 2\sqrt{2}[/tex]
b) [tex]\sqrt{3} * \sqrt{6} - \sqrt{32} = \sqrt{3*6} - \sqrt{16*2} = \sqrt{18} - 4\sqrt{2} = \sqrt{9*2} - 4\sqrt{2} = 3\sqrt{2} -4\sqrt{2} = -\sqrt{2}[/tex]
c) [tex]\sqrt{6} : \sqrt{2} - \sqrt{60} : \sqrt{5} = \sqrt{3} - \sqrt{12} = \sqrt{3} - 2\sqrt{3} = -\sqrt{3}[/tex]
d) [tex]\sqrt{2} * 2\sqrt{3} - \sqrt{42} : \sqrt{7} = 2\sqrt{6} - \sqrt{6} = \sqrt{6}[/tex]
