What is the simplified result of sqrt(-25) * sqrt(-81)?

To simplify the expression ( \sqrt{-25} \times \sqrt{-81} ), we need to use the properties of square roots and imaginary numbers.

First, recognize that the square root of a negative number can be expressed using the imaginary unit ( i ), where ( i^2 = -1 ). Thus, we can rewrite ( \sqrt{-25} ) and ( \sqrt{-81} ) as follows:

[

\sqrt{-25} = \sqrt{25 \cdot -1} = \sqrt{25} \cdot \sqrt{-1} = 5i

]

[

\sqrt{-81} = \sqrt{81 \cdot -1} = \sqrt{81} \cdot \sqrt{-1} = 9i

]

Now, we can multiply these two results together:

[

\sqrt{-25} \times \sqrt{-81} = (5i) \times (9i) = 45i^2

]

Since ( i^2 = -1 ), we substitute to get:

[

45i^2 = 45(-1) = -45

]

Thus, the simplified result