The value of `root (3) (-2300) xx root (3) (5290)` is

Options

A. `-270`
B. 230
C. -230
D. -529

Answer

To solve the expression \( \sqrt[3]{-2300} \times \sqrt[3]{5290} \), we can follow these steps:

### Step 1: Rewrite the expression
We start with the expression:
\[ \sqrt[3]{-2300} \times \sqrt[3]{5290} \]
Using the property of cube roots, we can combine them:
\[ \sqrt[3]{-2300 \times 5290} \]

### Step 2: Calculate the product inside the cube root
Next, we need to calculate the product \(-2300 \times 5290\):
\[ -2300 \times 5290 = -12137000 \]
Now we have:
\[ \sqrt[3]{-12137000} \]

### Step 3: Factor the number inside the cube root
To simplify \(-12137000\), we can factor it:
\[ -12137000 = -1 \times 12137 \times 1000 \]
Since \(1000 = 10^3\), we can rewrite it as:
\[ -1 \times 12137 \times 10^3 \]

### Step 4: Apply the cube root
Now we can apply the cube root:
\[ \sqrt[3]{-1 \times 12137 \times 10^3} = \sqrt[3]{-1} \times \sqrt[3]{12137} \times \sqrt[3]{10^3} \]
We know that:
\[ \sqrt[3]{-1} = -1 \quad \text{and} \quad \sqrt[3]{10^3} = 10 \]
Thus, we have:
\[ -1 \times \sqrt[3]{12137} \times 10 \]

### Step 5: Simplify the expression
Now we can simplify:
\[ -10 \times \sqrt[3]{12137} \]

### Step 6: Final answer
The final expression is:
\[ -10 \times \sqrt[3]{12137} \]