` (sqrt(-3))(sqrt(-5))` is equal to

Options

A. `sqrt15`
B. `-sqrt15`
C. `isqrt15`
D. `sqrt5`

Answer

To solve the expression \( \sqrt{-3} \cdot \sqrt{-5} \), we can follow these steps:

### Step 1: Rewrite the square roots
We start by rewriting the square roots of negative numbers using the imaginary unit \( i \), where \( i = \sqrt{-1} \).

\[ \sqrt{-3} = \sqrt{3} \cdot \sqrt{-1} = \sqrt{3} \cdot i \]
\[ \sqrt{-5} = \sqrt{5} \cdot \sqrt{-1} = \sqrt{5} \cdot i \]

### Step 2: Substitute back into the expression
Now we substitute these expressions back into the original product:

\[ \sqrt{-3} \cdot \sqrt{-5} = (\sqrt{3} \cdot i) \cdot (\sqrt{5} \cdot i) \]

### Step 3: Simplify the expression
Next, we can simplify the product:

\[ = \sqrt{3} \cdot \sqrt{5} \cdot i \cdot i \]

### Step 4: Calculate \( i \cdot i \)
Recall that \( i \cdot i = i^2 = -1 \):

\[ = \sqrt{3} \cdot \sqrt{5} \cdot (-1) \]

### Step 5: Combine the square roots
Now we can combine the square roots:

\[ = -(\sqrt{3 \cdot 5}) = -\sqrt{15} \]

### Final Result
Thus, the final result is:

\[ \sqrt{-3} \cdot \sqrt{-5} = -\sqrt{15} \]

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