Finding the Cube Root of .000216

To find the cube root of a number, we need to find a number that, when multiplied by itself twice, gives us the original number. In this case, we need to find the number that, when multiplied by itself twice, gives us 0.000216.

Step 1: Writing the Number in Decimal Form
The number given is 0.000216. To make it easier to work with, we can write it in decimal form as 216 × 10^(-6).

Step 2: Simplifying the Expression
Now, let's simplify the expression by taking the cube root of each part separately:
Cube root of 216 = 6, since 6 × 6 × 6 = 216.
Cube root of 10^(-6) = 10^(-2) = 0.01, since 0.01 × 0.01 × 0.01 = 0.000001.

Step 3: Combining the Results
To find the cube root of the original number, we need to combine the two results from step 2:
Cube root of 216 × 10^(-6) = 6 × 0.01 = 0.06.

Therefore, the cube root of 0.000216 is 0.06, which corresponds to option 'B'.

In summary:
Given number: 0.000216
Cube root of 216 = 6
Cube root of 10^(-6) = 0.01
Combining the results: 6 × 0.01 = 0.06