Evaluate `root3(216 xx (-343))`.

Options

A. `-45`
B. `-42`
C. `-47`
D. `-44`

Answer

To evaluate the expression \( \sqrt[3]{216 \times (-343)} \), we can follow these steps:

### Step 1: Break down the numbers
First, we need to express 216 and -343 in terms of their cube roots.

- \( 216 = 6^3 \) because \( 6 \times 6 \times 6 = 216 \).
- \( -343 = (-7)^3 \) because \( -7 \times -7 \times -7 = -343 \).

### Step 2: Rewrite the expression
Now we can rewrite the original expression using these identities:
\[ \sqrt[3]{216 \times (-343)} = \sqrt[3]{6^3 \times (-7)^3} \]

### Step 3: Apply the property of cube roots
Using the property of cube roots, we can separate the cube roots:
\[ \sqrt[3]{6^3 \times (-7)^3} = \sqrt[3]{6^3} \times \sqrt[3]{(-7)^3} \]

### Step 4: Simplify the cube roots
Now we can simplify each cube root:
\[ \sqrt[3]{6^3} = 6 \quad \text{and} \quad \sqrt[3]{(-7)^3} = -7 \]

### Step 5: Multiply the results
Now we multiply the results from the previous step:
\[ 6 \times (-7) = -42 \]

### Final Answer
Thus, the value of \( \sqrt[3]{216 \times (-343)} \) is:
\[ \boxed{-42} \]

---