Analyze perfect cubes:
1^3 = 1
2^3 = 8
3^3 = 27
Since 12 is between 8 and 27, cube root of 12 is between 2 and 3.
You also know it is much closer to 2, since 12 is much closer to 8.
A good guess would be 2.25
(2.25)^3 = 11.39
This is close but slightly less than 12.
When you use your calculator you should get 2.2894.