Question

1. 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

Explicação

a) √8 × √6 = √8×6 = √48

mmc(48) = 2² . 2² . 3

√48 = √2².2².3 = 2.2√3 = 4√3

b) √2 × √27 = √2×27 = √54

mmc(54) = 2 . 3² . 3

√54 = √2.3².3 = 3√3.2 = 3√6

c) √42 × √28 = √42×28 = √1176

mmc(1176) = 2² . 2 . 3 . 7²

√1176 = √2².2.3.7² = 2.7√2.3 = 14√6

d) 2√10 × 5√30 = 2×5√10×30 = 10√300

mmc(300) = 2² . 3 . 5²

10√300 = 10√2².3.5² = 10.2.5√3 = 100√3

e) √8 × √12 × 10√3 = 10√8×12×3 = 10√288

mmc(288) = 2² . 2² . 2 . 3²

10√288 = 10√2².2².2.3² = 10.2.2.3√2 = 120√2

f) 6√7 × 5√2 × 8√21 = 6×5×8√7×2×21 = 240√294

mmc(294) = 2 . 3 . 7²

240√2.3.7² = 240.7√2.3 = 1680√6

respostas:

a)4√3

b)3√6

c)14√6

d)100√3

e)120√6

f)1680√6