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

Options

A. `0.027`
B. `0.008`
C. `0.001`
D. `0.421875`

Answer

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

### Step 1: Calculate the cube roots
First, we need to find the cube roots of \(0.064\) and \(0.027\).

- The cube root of \(0.064\):
\[ \sqrt[3]{0.064} = \sqrt[3]{\frac{64}{1000}} = \frac{\sqrt[3]{64}}{\sqrt[3]{1000}} = \frac{4}{10} = 0.4 \]

- The cube root of \(0.027\):
\[ \sqrt[3]{0.027} = \sqrt[3]{\frac{27}{1000}} = \frac{\sqrt[3]{27}}{\sqrt[3]{1000}} = \frac{3}{10} = 0.3 \]

### Step 2: Substitute the values into the equation
Now we substitute these values back into the equation:
\[ 0.4 = 0.3 + \sqrt[3]{?} \]

### Step 3: Isolate the cube root
Next, we isolate \( \sqrt[3]{?} \):
\[ \sqrt[3]{?} = 0.4 - 0.3 = 0.1 \]

### Step 4: Cube both sides to solve for ?
Now we cube both sides to find the value of \( ? \):
\[ ? = (0.1)^3 = 0.001 \]

### Final Answer
The value of \( ? \) is \( 0.001 \).

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