If `(sqrt(x))/(sqrt(0.0064))=root3(0.008)`, then find the value of x.

Answer

To solve the equation \(\frac{\sqrt{x}}{\sqrt{0.0064}} = \sqrt[3]{0.008}\), we will follow these steps:

### Step 1: Simplify the right side of the equation
First, we need to simplify the cube root on the right side:

\[ \sqrt[3]{0.008} = \sqrt[3]{\frac{8}{1000}} = \frac{\sqrt[3]{8}}{\sqrt[3]{1000}} = \frac{2}{10} = 0.2 \]

### Step 2: Simplify the left side of the equation
Next, we simplify the left side:

\[ \frac{\sqrt{x}}{\sqrt{0.0064}} = \frac{\sqrt{x}}{\sqrt{\frac{64}{10000}}} = \frac{\sqrt{x}}{\frac{8}{100}} = \sqrt{x} \cdot \frac{100}{8} = \sqrt{x} \cdot 12.5 \]

### Step 3: Set up the equation
Now we can set up the equation:

\[ \sqrt{x} \cdot 12.5 = 0.2 \]

### Step 4: Solve for \(\sqrt{x}\)
To isolate \(\sqrt{x}\), divide both sides by 12.5:

\[ \sqrt{x} = \frac{0.2}{12.5} \]

Calculating the right side:

\[ \sqrt{x} = \frac{0.2}{12.5} = 0.016 \]

### Step 5: Square both sides to find \(x\)
Now, square both sides to solve for \(x\):

\[ x = (0.016)^2 \]

Calculating \(0.016^2\):

\[ x = 0.000256 \]

### Final Answer
Thus, the value of \(x\) is:

\[ \boxed{0.000256} \]

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