Question

find the square root of the number.\\(\sqrt{-64}\\)\
the square root is \\(\square\\).

Explanation:

Step1: Recall imaginary unit definition

The imaginary unit \( i \) is defined as \( i = \sqrt{-1} \).

Step2: Simplify the square root

We can rewrite \( \sqrt{-64} \) as \( \sqrt{64 \times (-1)} \). Using the property of square roots \( \sqrt{ab}=\sqrt{a}\times\sqrt{b} \) (for \( a\geq0, b\) as a real number here), we get \( \sqrt{64}\times\sqrt{-1} \). Since \( \sqrt{64} = 8 \) and \( \sqrt{-1}=i \), then \( \sqrt{-64}=8i \).

Answer:

\( 8i \)