`root3(125 xx 64)=?`

Options

A. 100
B. 40
C. 20
D. 30

Answer

To solve the problem \( \sqrt[3]{125 \times 64} \), we can follow these steps:

### Step-by-Step Solution:

1. **Calculate the product inside the cube root**:
\[ 125 \times 64 \]

2. **Factor 125 and 64 into cubes**:
- \( 125 = 5^3 \) (since \( 5 \times 5 \times 5 = 125 \))
- \( 64 = 4^3 \) (since \( 4 \times 4 \times 4 = 64 \))

3. **Rewrite the product using the factored forms**:
\[ 125 \times 64 = 5^3 \times 4^3 \]

4. **Combine the bases under a single cube**:
\[ 5^3 \times 4^3 = (5 \times 4)^3 = 20^3 \]

5. **Apply the cube root**:
\[ \sqrt[3]{20^3} \]

6. **Simplify the expression**:
Since the cube root and the cube cancel each other out, we have:
\[ \sqrt[3]{20^3} = 20 \]

### Final Answer:
\[ \sqrt[3]{125 \times 64} = 20 \]