Question

151. Выполните указанные действия:
1) 6√2+5√18
3)√2+√50-√18
5)3√48+√27+√12


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Answer 1

$\displaystyle\bf\\1)\\\\6\sqrt{2}+5\sqrt{18} =6\sqrt{2} +5\sqrt{9\cdot 2} =6\sqrt{2} +5\cdot 3\sqrt{2} =6\sqrt{2} +15\sqrt{2} =21\sqrt{2} \\\\\\3)\\\\\sqrt{2} +\sqrt{50} -\sqrt{18} =\sqrt{2} +\sqrt{25\cdot 2} -\sqrt{9\cdot 2} =\sqrt{2} +5\sqrt{2} -3\sqrt{2} =4\sqrt{2} \\\\\\5)\\\\3\sqrt{48} +\sqrt{27} +\sqrt{12} =3\sqrt{16\cdot 3}+\sqrt{9\cdot 3} +\sqrt{4\cdot 3} =\\\\=3\cdot 4\sqrt{3} +3\sqrt{3} +2\sqrt{3} =12\sqrt{3} +5\sqrt{3} =17\sqrt{3 }$