Question

express the number in terms of \\(i\\).

\\\sqrt{-45}\\

\\(\sqrt{-45} = \square\\)
(simplify your answer. type an exact answer, using radicals and \\(i\\) as needed.)

Explanation:

Separate the negative sign

Using the Imaginary Numbers knowledge point

$$ \sqrt{-45} = \sqrt{-1 \cdot 45} = \sqrt{-1} \cdot \sqrt{45} = i\sqrt{45} $$

Simplify the radical

Using the Product Rule for Radicals knowledge point

$$ \sqrt{45} = \sqrt{9 \cdot 5} = \sqrt{9} \cdot \sqrt{5} = 3\sqrt{5} $$

Combine the results

Using the Imaginary Numbers and Product Rule for Radicals knowledge points

$$ \sqrt{-45} = 3i\sqrt{5} $$

Answer:

Express the number in terms of \(i\).

\(\sqrt{-45} =\) <blank>\(3i\sqrt{5}\)</blank>