Спростіть вираз: 5√2+3√50-7√18

5\sqrt{2} +3\sqrt{50} -7\sqrt{18} =-\sqrt{2}

5\sqrt{2} +3\sqrt{50} -7\sqrt{18} =5\sqrt{2} +3\sqrt{25\cdot2} -7\sqrt{9\cdot2} =

=5\sqrt{2} +3\sqrt{5^2\cdot2} -7\sqrt{3^2\cdot2} =5\sqrt{2} +3\cdot5\sqrt{2} -7\cdot3\sqrt{2} =

=5\sqrt{2} +15\sqrt{2} -21\sqrt{2} =(5+15-21)\cdot\sqrt{2} =-1\cdot\sqrt{2} =\boxed{-\sqrt{2} }