Question

Calculati: , va rog mult mă nevoie​

Answer 1

Explicație pas cu pas:

$a)2 \sqrt{18} + \sqrt{50} + 3 \sqrt{32} = \\ \\ 2 \times 3 \sqrt{2} + 5 \sqrt{2} + 3 \times 4 \sqrt{2} = \\ \\ 6 \sqrt{2} + 5 \sqrt{2} + 12 \sqrt{2} = \\ \\ (6 + 5 + 12) \sqrt{2} = \\ \\ 23 \sqrt{2}$

$b)4 \sqrt{12} - 2 \sqrt{27} + \sqrt{75} = \\ \\ 4 \times 2 \sqrt{3} - 2 \times 3 \sqrt{3} + 5 \sqrt{3} = \\ \\ 8 \sqrt{3} - 6 \sqrt{3} + 5 \sqrt{3} = \\ \\ (8 - 6 + 5) \sqrt{3} = \\ \\ (13 - 6) \sqrt{3} = \\ \\ 7 \sqrt{3}$

$c)3 \sqrt{20} - 2 \sqrt{45} + 4 \sqrt{80} = \\ \\ 3 \times 2 \sqrt{5} - 2 \times 3 \sqrt{5} + 4 \times 4 \sqrt{5} = \\ \\ 6 \sqrt{5} - 6 \sqrt{5} + 16 \sqrt{5} = \\ \\ 16 \sqrt{5}$

$d)3 \sqrt{150} - \sqrt{54} - 5 \sqrt{96} = \\ \\ 3 \times 5 \sqrt{6} - 3 \sqrt{6} - 5 \times 4 \sqrt{6} = \\ \\ 15 \sqrt{6} - 3 \sqrt{6} - 20 \sqrt{6} = \\ \\ (15 - 3 - 20) \sqrt{6} = \\ \\ (15 - 23) \sqrt{6} = \\ \\ - 8 \sqrt{6}$

$e) - 4 \sqrt{75} + 3 \sqrt{48} - \sqrt{108} = \\ \\ - 4 \times 5 \sqrt{3} + 3 \times 4 \sqrt{3} - 6 \sqrt{3} = \\ \\ - 20 \sqrt{3} + 12 \sqrt{3} - 6 \sqrt{3} = \\ \\ ( - 20 + 12 - 6) \sqrt{3} = \\ \\ ( - 26 + 12) \sqrt{3} = \\ \\ - 14 \sqrt{3}$