Question

Calcular as expressões:

A) 4√8+2+3√512

B)9√8+7√128+6

C) (5√2)⁵

Answer 1

Resposta:

a) 2 + 56√2

b) 6 + 74√2

c) 12500√2

Explicação passo a passo:

a) 4√8+2+3√512

√8:

Fatorar 8

8 | 2

4 | 2

2 | 2

1 | 1

8 = 2 . 2 . 2 = 2³ = 2.2²

√8 = √2.2² = √2.√2² =2.√2=2√2

√512:

Fatorar 512

512 | 2

256 | 2

128 | 2

64 | 2

32 | 2

16 | 2

8 | 2

4 | 2

2 | 2

1 | 1

512= 2 . 2 . 2 . 2 . 2 . 2 . 2 . 2 . 2 = 2⁹ = 2.2⁸

√512 = √2.2⁸=√2.√2⁸=√2.2⁸/²=2⁴√2=16√2

4√8+2+3√512 =

4.(2√2)+2+3.(16√2) =

8√2 + 2 + 48√2=

2 + (8+48)√2=

2+56√2

b) 9√8+7√128+6

√8 = 2√2 (ver exercício a)

√128:

Fatorar 128

128 | 2

64 | 2

32 | 2

16 | 2

8 | 2

4 | 2

2 | 2

1 | 1

128 = 2 . 2 . 2 . 2 . 2 . 2 . 2 = 2⁷ = 2.2⁶

√128 = √2.2⁶ = √2.√2⁶ = 2⁶/²√2 = 2³√2 = 8√2

9√8+7√128+6 =

9(2√2)+7(8√2)+6 =

18√2 + 56√2 +6 =

6 + (18+56)√2 =

6 + 74√2

c)  

(5√2)⁵ =  

5⁵√2⁵ = 5.5.5.5.5.√2.2⁴ = 3125√2.√2⁴ = 3125.2⁴/².√2 = 3125.2².√2 = 12500√2

Propriedade:

ᵃ√bⁿ = bⁿ/ᵃ