`(0.06xx0.06xx0.06-0.05xx0.05xx0.05)/(0.06xx0.06+0.06xx0.05+0.05xx0.05)` gives

Options

A. 0.01
B. 0.001
C. 0.1
D. 0.02

Answer

To solve the expression \((0.06 \times 0.06 \times 0.06 - 0.05 \times 0.05 \times 0.05) / (0.06 \times 0.06 + 0.06 \times 0.05 + 0.05 \times 0.05)\), we can use the algebraic identity for the difference of cubes and the sum of cubes.

### Step-by-Step Solution:

1. **Identify a and b**:
Let \( a = 0.06 \) and \( b = 0.05 \).

2. **Use the difference of cubes formula**:
The difference of cubes can be expressed as:
\[ a^3 - b^3 = (a - b)(a^2 + ab + b^2) \]
Therefore, we can rewrite the numerator:
\[ 0.06^3 - 0.05^3 = (0.06 - 0.05)(0.06^2 + 0.06 \times 0.05 + 0.05^2) \]
This simplifies to:
\[ 0.01(0.06^2 + 0.06 \times 0.05 + 0.05^2) \]

3. **Calculate the denominator**:
The denominator is:
\[ 0.06^2 + 0.06 \times 0.05 + 0.05^2 \]
This is the same expression we found in the numerator:
\[ 0.06^2 + 0.06 \times 0.05 + 0.05^2 \]

4. **Substitute back into the expression**:
Now we can substitute back into our original expression:
\[ \frac{0.01(0.06^2 + 0.06 \times 0.05 + 0.05^2)}{0.06^2 + 0.06 \times 0.05 + 0.05^2} \]

5. **Simplify the expression**:
The \(0.06^2 + 0.06 \times 0.05 + 0.05^2\) terms cancel out:
\[ = 0.01 \]

### Final Answer:
The value of the expression is \(0.01\).