Start by finding the cube of 3.5 which is in between 3 and 4.
The answer would be 42.875
Since this number is too high, find the number in between 3 and 3.5, since if you use a number in-between 3.5 and 4, it would be too high. The number would 3.25
Now find the cube of 3.25 which is approximately 34.3
Since this number is also too high, find the number in between 3 and 3.25, which is 3.125
Now find the cube of 3.125 which is 30.5
Since that is too high find the number in between 3 and 3.125, which is 3.0625
Find the cube of 3.0625, which is approximately 28.7.
Since 28.7 is too low, find the number in between 3.0625 and 3.125 since 3.125 is the highest number we have that comes closest to 30.
(3.125 - 3.0625 = 0.625; 0.625/2 = 0.3125; 3.0625 + 0.3125 = 3.09375)
The number would then be 3.09375
Find the cube of 3.09375
The answer would be about 29.61118
Find the number in between 3.09375 and 3.125
That number is 3.109375
3.109375 cubed is 30.06210
Congratulations! Since 30.06 has a value in the hundredths place that gets you close to 30. The sides of the cube would be 3.109375.
(Technically you can keep repeating the steps forever to find the "exact" answer, but that is impossible in your lifetime or the entire life of the universe)