Question

use square root symbol to solve x^2 = -64

Answer 1

To solve the equation \( x^2 = -64 \), we can take the square root of both sides. However, since the right side is negative, we will need to use imaginary numbers.

Starting from \( x^2 = -64 \), we can write:

\[
x = \pm \sqrt{-64}
\]

Using the property of imaginary numbers, where \( \sqrt{-1} = i \) (the imaginary unit), we can rewrite \( \sqrt{-64} \):

\[
\sqrt{-64} = \sqrt{64} \cdot \sqrt{-1} = 8i
\]

Thus, we have two solutions:

\[
x = 8i \quad \text{or} \quad x = -8i
\]

So the solutions to the equation \( x^2 = -64 \) are:

\[
x = 8i \quad \text{and} \quad x = -8i
\]