Question

calculați, dupa ce ati scos factorii de sub radicali
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Answer 1

Explicație pas cu pas:

$a)( \sqrt{450} - \sqrt{200}) - ( \sqrt{1250} - \sqrt{1800}) = \\ \\ 15 \sqrt{2} - 10 \sqrt{2} - (25 \sqrt{2} - 30 \sqrt{2}) = \\ \\ 15 \sqrt{2} - 10 \sqrt{2} - ( - 5 \sqrt{2}) = \\ \\ 15 \sqrt{2} - 10 \sqrt{2} + 5 \sqrt{2} = \\ \\ (15 - 10 + 5) \sqrt{2} = \\ \\ (20 - 10) \sqrt{2} = \\ \\ 10 \sqrt{2}$

$b) \sqrt{1805} - ( \sqrt{1620} - \sqrt{845}) - \sqrt{720} = \\ \\ 19 \sqrt{5} - (18 \sqrt{5} - 13 \sqrt{5}) - \sqrt{720} = \\ \\ 19 \sqrt{5} - 5 \sqrt{5} - 12 \sqrt{5} = \\ \\ (19 - 5 - 12) \sqrt{5} = \\ \\ (19 - 17) \sqrt{5} = \\ \\ 2 \sqrt{5}$

$c) \sqrt{160} - ( \sqrt{810} - \sqrt{9610} + \sqrt{6760}) = \\ \\ 4 \sqrt{10} - (9 \sqrt{10} - 31 \sqrt{10} + 26 \sqrt{10}) = \\ \\ 4 \sqrt{10} - (9 - 31 + 26) \sqrt{10} = \\ \\ 4 \sqrt{10} - (35 - 31) \sqrt{10} = \\ \\ 4 \sqrt{10} - 4 \sqrt{10} = \\ \\ 0$

$d) \sqrt{4375} - ( \sqrt{3087} + \sqrt{4732} - \sqrt{2268}) = \\ \\ 25 \sqrt{7} - (21 \sqrt{7} + 26 \sqrt{7} - 18 \sqrt{7}) = \\ \\ 25 \sqrt{7} - (47 - 18) \sqrt{7} = \\ \\ 25 \sqrt{7} - 29 \sqrt{7} = \\ \\ - 4 \sqrt{7}$