Question
\( 1 \leftarrow \quad \begin{array}{l}\text { Multiply. } \\ (\sqrt{-36})(\sqrt{-9}) \\ (\sqrt{-36})(\sqrt{-9})=\square \text { (Simplify your answer.) }\end{array} \)
Ask by Bernard Phillips. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified answer is -18.
Solution
To simplify (√(-36)) (√(-9)), first express each square root in terms of i (where i² = -1):
√(-36) = √36 × i = 6i
√(-9) = √9 × i = 3i
Now multiply:
(6i)(3i) = 18i²
Since i² = -1, this becomes:
18(-1) = -18
The simplified answer is -18.
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Simplify this solution Extra Insights
To solve \((\sqrt{-36})(\sqrt{-9})\), we first recognize that the square root of a negative number involves imaginary numbers. We can rewrite it as: \(\sqrt{-36} = \sqrt{36} \cdot i = 6i\) \(\sqrt{-9} = \sqrt{9} \cdot i = 3i\) Now we can multiply them together: \((6i)(3i) = 18i^2\). Since \(i^2 = -1\), we can substitute that in: \(18i^2 = 18(-1) = -18\). Therefore, \((\sqrt{-36})(\sqrt{-9}) = -18\).
