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

Options

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

Answer

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

### Step 1: Rewrite the expression
We start with the expression:
\[ 3\sqrt{-2300} \times 3\sqrt{5290} \]
This can be rewritten as:
\[ (3\sqrt{-2300}) \times (3\sqrt{5290}) = 9 \times \sqrt{-2300} \times \sqrt{5290} \]

### Step 2: Combine the square roots
Since both terms are under square roots, we can combine them:
\[ 9 \times \sqrt{-2300 \times 5290} \]

### Step 3: Calculate the product inside the square root
Now, we need to calculate \(-2300 \times 5290\):
\[ -2300 \times 5290 = -12137000 \]
Thus, we have:
\[ 9 \times \sqrt{-12137000} \]

### Step 4: Factor out the negative sign
We can factor out the negative sign from the square root:
\[ 9 \times \sqrt{-1 \times 12137000} = 9 \times i \times \sqrt{12137000} \]
where \(i\) is the imaginary unit.

### Step 5: Simplify \(\sqrt{12137000}\)
Next, we simplify \(\sqrt{12137000}\):
\[ 12137000 = 12137 \times 1000 \]
Thus:
\[ \sqrt{12137000} = \sqrt{12137} \times \sqrt{1000} = \sqrt{12137} \times 10\sqrt{10} \]

### Step 6: Combine the results
Now we can combine everything:
\[ 9 \times i \times 10 \times \sqrt{12137} \times \sqrt{10} = 90i \times \sqrt{12137 \times 10} \]

### Final Result
The final result is:
\[ 90i \times \sqrt{121370} \]