Question

1) Reduza os termos semelhantes
A) √8+√18=
B) √27+√75+5√3
C)√125+2√5
D)√25x+√16x+√49x
E)√4a+9√a-√64a-√9a
F)√2+10√50
G)√3+8√12-7√27

Answer 1

$a) \: \sqrt{8} + \sqrt{18} = \sqrt{2 \times 4} + \sqrt{2 \times 9} = \\ \sqrt{2} \times \sqrt{4} + \sqrt{2} \times \sqrt{9} = \sqrt{2} \times 2 + \sqrt{2} \times 3 = \\ 2 \sqrt{2} + 3 \sqrt{2} = 5 \sqrt{2}$
$b) \: \sqrt{27} + \sqrt{75} + 5 \sqrt{3} = \\ \sqrt{3 \times 9} + \sqrt{3 \times 25} + 5 \sqrt{3} = \\ \sqrt{3} \times \sqrt{9} + \sqrt{3} \times \sqrt{25} + 5 \sqrt{3} \\ \sqrt{3} \times 3 + \sqrt{3} \times 5 + 5 \sqrt{3} = \\ 3 \sqrt{3 } + 5 \sqrt{3} + 5 \sqrt{3} = 13 \sqrt{3}$
$c) \: \sqrt{125} + 2 \sqrt{5} = \\ \sqrt{5 \times 25} + 2 \sqrt{5} = \\ \sqrt{5} \times \sqrt{25} + 2 \sqrt{5} = \\ \sqrt{5} \times 5 + 2 \sqrt{5} = 5 \sqrt{5} + 2 \sqrt{5} = 7 \sqrt{5}$
$d) \: \sqrt{25x} + \sqrt{16x} + \sqrt{49x} = \\ 5 \sqrt{x} + 4 \sqrt{x} + 7 \sqrt{x} = 16 \sqrt{x}$
$e) \: \sqrt{4a} + 9 \sqrt{a} - \sqrt{64a} - \sqrt{9a} = \\ 2 \sqrt{a} + 9 \sqrt{a} - 8 \sqrt{a} - 3 \sqrt{a} = \\ 11 \sqrt{a} - 11 \sqrt{a} = 0$
$f) \: \sqrt{2} + 10 \sqrt{50} = \\ \sqrt{2} + 10 \sqrt{25 \times 2} = \sqrt{2} + 10 \times 5 \sqrt{2} = \\ \sqrt{2} + 50 \sqrt{2} = 51 \sqrt{2}$
$g) \: \sqrt{3} + 8 \sqrt{12} - 7 \sqrt{27} = \\ \sqrt{3} + 8 \sqrt{4 \times 3} - 7 \sqrt{9 \times 3} = \\ \sqrt{3} + 8 \times 2 \sqrt{3} - 7 \times 3 \sqrt{3} = \\ \sqrt{3} + 16 \sqrt{3} - 21 \sqrt{3} = - 4 \sqrt{3}$
Espero ter ajudado!