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 \( a \times 10^b \).

Learn how to calculate the cube root of the square root of 0.000064 with a detailed step-by-step solution. This problem involves basic arithmetic operations and root calculations. Suitable for students in Grades 7-9.

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