The value of `0.09 xx 3sqrt(0.000064)` is

Options

A. `0.036`
B. `0.00036`
C. `0.36`
D. None of these

Answer

To solve the problem, we need to calculate the value of \(0.09 \times \sqrt[3]{0.000064}\).

### Step 1: Calculate the cube root of \(0.000064\)

First, we will find the cube root of \(0.000064\).

\[ 0.000064 = 64 \times 10^{-6} \]

Now, we can find the cube root:

\[ \sqrt[3]{0.000064} = \sqrt[3]{64 \times 10^{-6}} = \sqrt[3]{64} \times \sqrt[3]{10^{-6}} \]

We know that:

\[ \sqrt[3]{64} = 4 \quad \text{(since \(4^3 = 64\))} \]
\[ \sqrt[3]{10^{-6}} = 10^{-2} = 0.01 \]

Thus,

\[ \sqrt[3]{0.000064} = 4 \times 0.01 = 0.04 \]

### Step 2: Multiply by \(0.09\)

Now, we will multiply \(0.09\) by the result from Step 1:

\[ 0.09 \times 0.04 \]

To multiply these two decimals, we can convert them to fractions:

\[ 0.09 = \frac{9}{100}, \quad 0.04 = \frac{4}{100} \]

Now, multiply the fractions:

\[ \frac{9}{100} \times \frac{4}{100} = \frac{36}{10000} \]

### Step 3: Convert to decimal

Now, we convert \(\frac{36}{10000}\) back to decimal:

\[ \frac{36}{10000} = 0.0036 \]

### Final Answer

Thus, the value of \(0.09 \times \sqrt[3]{0.000064}\) is:

\[ \boxed{0.0036} \]