Question

efetue cada multiplicação e simplifique o resultado.
A)√8 . √6
B)√2 . √27
C)√42 . √28
D)2√10 . 5√30
E)√8 . √12 . 10√3
F)6√7 . 5√2 . 8√21​

Answer 1

Resposta:

$a) \: \sqrt{8} \times \sqrt{6} \\ \sqrt{8 \times 6 } \\ \sqrt{48} \\ \sqrt{16 \times 3} \\ \sqrt{ {4}^{2} \times 3 } \\ \sqrt{ {4}^{2} } \sqrt{3} \\ = 4 \sqrt{3}$

$b) \: \sqrt{2} \times \sqrt{27} \\ \sqrt{2 \times 27} \\ \sqrt{54} \\ \sqrt{9 \times 6} \\ \sqrt{ {3}^{2} \times 6} \\ \sqrt{ {3}^{2} } \sqrt{6} \\ = 3 \sqrt{6}$

$c) \: \sqrt{42} \times \sqrt{28} \\ \sqrt{42 \times 28} \\ \sqrt{1176} \\ \sqrt{196 \times 6} \\ \sqrt{ {14}^{2} } \sqrt{6} \\ = 14 \sqrt{6}$

$d) \: 2 \sqrt{10} \times 5 \sqrt{30} \\ 10 \times \sqrt{10 \times 30} \\ 10 \sqrt{300} \\ 10 \sqrt{100 \times 3} \\ 10 \sqrt{ {10}^{2} \times 3 } \\ 10 \sqrt{ {10}^{2} } \sqrt{3} \\ 10 \times 10 \sqrt{3} \\ 100 \sqrt{3}$

$e) \: \sqrt{8} \times \sqrt{12} \times 10 \sqrt{3} \\ 2 \sqrt{2} \times 2 \sqrt{3} \times 10 \sqrt{3} \\ 2 \sqrt{2} \times 2 \times 3 \times 10 \\ 20 \sqrt{2} \times 2 \times 3 \\ 40 \sqrt{2} \times 3 \\ 120 \sqrt{2}$

$f) \: 6 \sqrt{7} \times 5 \sqrt{2} \times 8 \sqrt{21} \\ 240 \sqrt{7 \times 2 \times 21} \\ 240 \sqrt{294} \\ 240 \sqrt{49 \times 6} \\ 240 \sqrt{ {7}^{2} \times 6} \\ 240 \sqrt{ {7}^{2} } \sqrt{6} \\ 240 \times 7 \sqrt{6} \\ 1680 \sqrt{6}$