Simplify `sqrt5 sqrt(-3)`

Answer

To simplify the expression \( \sqrt{5} \sqrt{-3} \), follow these steps:

### Step 1: Rewrite the expression
We start with the expression:
\[ \sqrt{5} \sqrt{-3} \]

### Step 2: Use the property of square roots
We can use the property of square roots that states \( \sqrt{a} \sqrt{b} = \sqrt{ab} \). Thus, we can rewrite our expression as:
\[ \sqrt{5 \cdot (-3)} \]

### Step 3: Calculate the product inside the square root
Now, we compute the product:
\[ 5 \cdot (-3) = -15 \]
So, we have:
\[ \sqrt{-15} \]

### Step 4: Express the square root of a negative number
Since we have a negative number under the square root, we can express it using the imaginary unit \( i \), where \( i = \sqrt{-1} \). Therefore:
\[ \sqrt{-15} = \sqrt{15} \cdot \sqrt{-1} = \sqrt{15} \cdot i \]

### Step 5: Final expression
Thus, the simplified form of the original expression is:
\[ \sqrt{15} i \]

### Final Answer:
\[ \sqrt{5} \sqrt{-3} = \sqrt{15} i \]

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