To solve this problem, let's break it down step by step.

Step 1: Find $x$

We are given that: $x = \sqrt{0.000064}$

First, let's calculate the square root of $0.000064$.

$x = \sqrt{0.000064} = 0.008$

Step 2: Find the cube root of $x$

Next, we need to find $\text{root}(x, 3)$, which is the cube root of $x$.

[ \text{root}(x, 3) = \sqrt[3]{x} = \sqrt[3]{0.008} ]

$\text{root}(x, 3) = 0.2$

So, the final answer is $\text{root}(x, 3) = 0.2$.

Would you like further details or have any questions about the solution? Here are some related problems you might find interesting:

1. Find the cube root of $\sqrt{0.000001}$.
2. If $y = \sqrt{0.0001}$, find $\text{root}(y, 3)$.
3. Calculate the square root of $0.000016$ and then find its cube root.
4. Solve $x = \sqrt{0.004096}$ and find $\text{root}(x, 3)$.
5. Determine the cube root of $0.027$.

Tip: When dealing with roots, remember that the square root and cube root of a number can often be simplified by converting the number into a form like $a \times 10^b$.