Question

O valor de √1,777.../√0,111... é:

a) 4,444...
b) 4.
c) 4,777...
d) 3.
e) 4/3



se pude com a conta por favor

Answer 1

√1,77777 / √0,1111 =
√16/√9 / √1/√9 =
√16/3 / 1/3 =
3√16 / 3 =
√16 =
4

Alternativa B

Answer 2

1,777... = x
17,777... = 10x
-------------------
17,777... - 1,777... = 10x - x
16 = 9x
x = 16/9

0,111... = y
1,111... = 10y
-------------------
1,111... - 0,111... = 10y - y
1 = 9y
y = 1/9

√1,777.../√0,111... = (√16/9)/(√1/9)

(√16/√9)/(√1/√9) = (4/3)/(1/3)

(4/3).3 = 4

Resposta: Alternativa B.