Question

Use the square root symbol to solve x2= - 64. (1 point)
0 x= ‡8
• x=-8
• no real solution
• x = 8

Answer 1

The equation \(x^2 = -64\) indicates that \(x\) is the square root of a negative number. Since the square root of a negative number involves imaginary numbers, we proceed as follows:

1. Take the square root of both sides:
\[
x = \sqrt{-64}
\]

2. This can be expressed using the imaginary unit \(i\):
\[
x = \sqrt{64} \cdot \sqrt{-1} = 8i
\]

Thus, the solutions are:
\[
x = 8i \quad \text{and} \quad x = -8i
\]

Since there are no real solutions, the correct answer is:
**no real solution**.