Question

va rog ajutati-ma pls

Answer 1

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Answer 2

$11) \\ \\ a) \\ \\ \sqrt{108} \times ( \sqrt{432} - \sqrt{75} - \sqrt{48}) = \\ \\ 6 \sqrt{3} \times (12 \sqrt{3} - 5 \sqrt{3} - 4 \sqrt{3}) = \\ \\ 6 \sqrt{3} \times 3 \sqrt{3} = \\ \\ 6 \times 3 \sqrt{3 \times 3} = \\ \\ 6 \times 3 \sqrt{9} = \\ \\ 6 \times 3 \times 3 = \\ \\ 54$

$b) \\ \\ 3 \sqrt{242} \times ( \sqrt{288} - 2 \sqrt{50} - \sqrt{32}) = \\ \\ 3 \times 11 \sqrt{2}(12 \sqrt{2} - 2 \times 5 \sqrt{2} - 4 \sqrt{2}) = \\ \\ 3 \times 11 \sqrt{2}(12 \sqrt{2} - 10 \sqrt{2} - 4 \sqrt{2}) = \\ \\ 3 \times 11 \sqrt{2} \times - 2 \sqrt{2} = \\ \\ - 3 \times 11 \times 2 \sqrt{2 \times 2} = \\ \\ - 3 \times 11 \times 2 \sqrt{4} = \\ \\ - 3 \times 11 \times 2 \times 2 = \\ \\ - 132$

$c) \\ \\ 2 \sqrt{72} \times (5 \sqrt{8} - 7 \sqrt{32} + 6 \sqrt{18} - 3 \sqrt{50}) = \\ \\ 2 \times 6 \sqrt{2}(5 \times 2 \sqrt{2} - 7 \times 4 \sqrt{2} + 6 \times 3 \sqrt{2} - 3 \times 5 \sqrt{2}) = \\ \\ 2 \times 6 \sqrt{2}(10 \sqrt{2} - 28 \sqrt{2} + 18 \sqrt{2} - 15 \sqrt{2}) = \\ \\ 2 \times 6 \sqrt{2} \times - 15 \sqrt{2} = \\ \\ - 2 \times 6 \times 15 \sqrt{2 \times 2} = \\ \\ - 2 \times 6 \times 15 \sqrt{4} = \\ \\ - 2 \times 6 \times 15 \times 2 = \\ \\ - 360$

$12) \\ \\ a) \\ \\ \sqrt{12} \times ( \sqrt{108} - 2 \sqrt{48}) - \sqrt{18} \times ( \sqrt{288} - \sqrt{72}) = \\ \\ 2 \sqrt{3}(6 \sqrt{3} - 2 \times 4 \sqrt{3}) - \sqrt{18}( \sqrt{288} - \sqrt{72}) = \\ \\ 2 \sqrt{3}(6 \sqrt{3} - 8 \sqrt{3}) - \sqrt{18}( \sqrt{288} - \sqrt{72}) = \\ \\ 2 \sqrt{3} \times - 2 \sqrt{3} - 3 \sqrt{2}(12 \sqrt{2} - 6 \sqrt{2}) = \\ \\ 2 \sqrt{3} \times - 2 \sqrt{3} - 3 \sqrt{2} \times 6 \sqrt{2} = \\ \\ - 2 \times 2 \sqrt{3 \times 3} - 3 \sqrt{2} \times 6 \sqrt{2} = \\ \\ - 2 \times 2 \sqrt{9} - 3 \sqrt{2} \times 6 \sqrt{2} = \\ \\ - 2 \times 2 \times 3 - 3 \sqrt{2} \times 6 \sqrt{2} = \\ \\ - 12 - 3 \times 6 \sqrt{2 \times 2} = \\ \\ - 12 - 3 \times 6 \sqrt{4} = \\ \\ - 12 - 3 \times 6 \times 2 = \\ \\ - 12 - 36 = \\ \\ - 48$

$b) \\ \\ \sqrt{18} \times (3 \sqrt{50} + \sqrt{162}) - \sqrt{12} \times ( \sqrt{432} - \sqrt{192}) = \\ \\ 3 \sqrt{2}(3 \times 5 \sqrt{2} + 9 \sqrt{2}) - \sqrt{12}( \sqrt{432} - \sqrt{192} ) = \\ \\ 3 \sqrt{2}(15 \sqrt{2} + 9 \sqrt{2}) - \sqrt{12}( \sqrt{432} - \sqrt{192}) = \\ \\ 3 \sqrt{2} \times 24 \sqrt{2} - 2 \sqrt{3}(12 \sqrt{3} - 8 \sqrt{3}) = \\ \\ 3 \sqrt{2} \times 24 \sqrt{2} - 2 \sqrt{3} \times 4 \sqrt{3} = \\ \\ 3 \times 24 \sqrt{2 \times 2} - 2 \sqrt{3} \times 4 \sqrt{3} = \\ \\ 3 \times 24 \sqrt{4} - 2 \sqrt{3} \times 4 \sqrt{3} = \\ \\ 3 \times 24 \times 2 - 2 \sqrt{3} \times 4 \sqrt{3} = \\ \\ 144 - 2 \sqrt{3} \times 4 \sqrt{3} = \\ \\ 144 - 2 \times 4 \sqrt{3 \times 3} = \\ \\ 144 - 2 \times 4 \sqrt{9} = \\ \\ 144 - 2 \times 4 \times 3 = \\ \\ 144 - 24 = \\ \\ 120$

$c) \\ \\ ( \sqrt{360} + 2 \sqrt{2} \times \sqrt{405}) \times ( \sqrt{810} - \sqrt{20} \times \sqrt{162}) = \\ \\ (6 \sqrt{10} + 2 \sqrt{2} \times 9 \sqrt{5})( \sqrt{810} - \sqrt{20} \times \sqrt{162}) = \\ \\ (6 \sqrt{10} + 2 \times 9 \sqrt{2 \times 5})( \sqrt{810} - \sqrt{20} \times \sqrt{162}) = \\ \\ (6 \sqrt{10} + 2 \times 9 \sqrt{10})( \sqrt{810} - \sqrt{20} \times \sqrt{162}) = \\ \\ (6 \sqrt{10} + 18 \sqrt{10})( \sqrt{810} - \sqrt{20} \times \sqrt{162}) = \\ \\ 24 \sqrt{10}(9 \sqrt{10} - 2 \sqrt{5} \times 9 \sqrt{2}) = \\ \\ 24 \sqrt{10}(9 \sqrt{10} - 2 \times 9 \sqrt{5 \times 2}) = \\ \\ 24 \sqrt{10}(9 \sqrt{10} - 2 \times 9 \sqrt{10}) = \\ \\ 24 \sqrt{10}(9 \sqrt{10} - 18 \sqrt{10}) = \\ \\ 24 \sqrt{10} \times - 9 \sqrt{10} = \\ \\ - 24 \times 9 \sqrt{10 \times 10} = \\ \\ - 24 \times 9 \sqrt{100} = \\ \\ - 24 \times 9 \times 10 = \\ \\ - 2160$

$d) \\ \\ 2 \sqrt{48} \times (5 \sqrt{27} - 6 \sqrt{48} + 7 \sqrt{12} - 4 \sqrt{75}) = \\ \\ 2 \times 4 \sqrt{3}(5 \times 3 \sqrt{3} - 6 \times 4 \sqrt{3} + 7 \times 2 \sqrt{3} - 4 \times 5 \sqrt{3}) = \\ \\ 2 \times 4 \sqrt{3}(15 \sqrt{3} - 24 \sqrt{3} + 14 \sqrt{3} - 20 \sqrt{3}) = \\ \\ 2 \times 4 \sqrt{3} \times - 15 \sqrt{3} = \\ \\ - 2 \times 4 \times 15 \sqrt{3 \times 3} = \\ \\ - 2 \times 4 \times 15 \sqrt{9} = \\ \\ - 2 \times 4 \times 15 \times 3 = \\ \\ - 360$