If `sqrt(root3(0.000001xx x))=0.5` then find the value of x.

Options

A. `15625`
B. `15.625`
C. `16625`
D. `16.625`

Answer

To solve the equation \( \sqrt[3]{0.000001 \cdot x} = 0.5 \), we will follow these steps:

### Step 1: Remove the cube root
To eliminate the cube root, we will cube both sides of the equation:

\[ \left(\sqrt[3]{0.000001 \cdot x}\right)^3 = (0.5)^3 \]

This simplifies to:

\[ 0.000001 \cdot x = 0.125 \]

### Step 2: Isolate x
Next, we will isolate \( x \) by dividing both sides by \( 0.000001 \):

\[ x = \frac{0.125}{0.000001} \]

### Step 3: Simplify the division
To simplify \( \frac{0.125}{0.000001} \), we can convert \( 0.125 \) to a fraction:

\[ 0.125 = \frac{125}{1000} = \frac{1}{8} \]

Now substituting this into our equation gives:

\[ x = \frac{\frac{1}{8}}{0.000001} \]

### Step 4: Convert \( 0.000001 \) to scientific notation
We can express \( 0.000001 \) as \( 10^{-6} \):

\[ x = \frac{\frac{1}{8}}{10^{-6}} = \frac{1}{8} \cdot 10^{6} \]

### Step 5: Multiply
Now, we can multiply:

\[ x = \frac{10^6}{8} \]

### Step 6: Simplify further
Calculating \( \frac{10^6}{8} \):

\[ x = 125000 \]

Thus, the value of \( x \) is:

\[ \boxed{125000} \]

---