The value of ? In `root(3)(0.064) = root(3)(0.027) div root(3)(?)` is

Options

A. `0.027`
B. `0.08`
C. `0.001`
D. `0.421875`

Answer

To solve the equation \( \sqrt[3]{0.064} = \frac{\sqrt[3]{0.027}}{\sqrt[3]{?}} \), we will follow these steps:

### Step 1: Rewrite the equation
We start with the equation:
\[ \sqrt[3]{0.064} = \frac{\sqrt[3]{0.027}}{\sqrt[3]{?}} \]
We can rewrite this as:
\[ \sqrt[3]{0.064} \cdot \sqrt[3]{?} = \sqrt[3]{0.027} \]

### Step 2: Remove the cube root
To eliminate the cube roots, we can cube both sides of the equation:
\[ 0.064 \cdot ? = 0.027 \]

### Step 3: Isolate the question mark
Now, we can isolate \( ? \) by dividing both sides by \( 0.064 \):
\[ ? = \frac{0.027}{0.064} \]

### Step 4: Perform the division
Next, we perform the division:
\[ ? = \frac{0.027}{0.064} = \frac{27}{64} \]

### Step 5: Convert to decimal
Now, we convert \( \frac{27}{64} \) to decimal:
\[ \frac{27}{64} = 0.421875 \]

### Conclusion
Thus, the value of \( ? \) is:
\[ ? = 0.421875 \]