If `a<0, b>0,` then `sqrta. sqrtb` is equal to :

Options

A. `isqrt(|a|b)`
B. `isqrt(|a||b|)`
C. `isqrt(|a||b|)`
D. `-sqrt(|a||b|)`

Explanation

To solve the problem, we need to analyze the expression \(\sqrt{a} \cdot \sqrt{b}\) given the conditions \(a < 0\) and \(b > 0\).

### Step-by-Step Solution:

1. **Identify the Values of a and b**:
- We know that \(a < 0\) means \(a\) is a negative number.
- We know that \(b > 0\) means \(b\) is a positive number.

2. **Understanding the Square Roots**:
- The square root of a negative number is not a real number. Instead, it is expressed in terms of imaginary numbers.
- Specifically, \(\sqrt{a}\) can be written as \(\sqrt{-|a|} = i\sqrt{|a|}\) since \(a\) is negative.

3. **Calculating \(\sqrt{a}\)**:
- Since \(a < 0\), we can express \(\sqrt{a}\) as:
\[ \sqrt{a} = \sqrt{-|a|} = i\sqrt{|a|} \]

4. **Calculating \(\sqrt{b}\)**:
- Since \(b > 0\), the square root of \(b\) is simply:
\[ \sqrt{b} = \sqrt{b} \]

5. **Multiplying the Square Roots**:
- Now, we multiply \(\sqrt{a}\) and \(\sqrt{b}\):
\[ \sqrt{a} \cdot \sqrt{b} = (i\sqrt{|a|}) \cdot (\sqrt{b}) = i\sqrt{|a|b} \]

6. **Final Expression**:
- Therefore, the final expression for \(\sqrt{a} \cdot \sqrt{b}\) is:
\[ \sqrt{a} \cdot \sqrt{b} = i\sqrt{|a|b} \]

### Conclusion:
Thus, if \(a < 0\) and \(b > 0\), then \(\sqrt{a} \cdot \sqrt{b} = i\sqrt{|a|b}\).