Determine if the given square root evaluates to a real number.
$\sqrt{-64}$

• A. Real
• B. Not Real
• C. Cannot be determined

Answer: (B)

Verified step by step guidance

1. Recall that the square root of a number \(a\), written as \(\sqrt{a}\), is defined as a real number \(b\) such that \(b^2 = a\), provided \(a\) is non-negative.
2. Identify the number inside the square root: here it is \(-64\), which is a negative number.
3. Understand that in the set of real numbers, the square root of a negative number is not defined because no real number squared gives a negative result.
4. Therefore, \(\sqrt{-64}\) does not evaluate to a real number; it is considered an imaginary or complex number.
5. Conclude that the expression \(\sqrt{-64}\) is not real.