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 number which, when squared, gives \(a\).
2. Understand that for real numbers, the square root function \(\sqrt{a}\) is only defined when \(a \geq 0\) because the square of any real number is non-negative.
3. Look at the given expression \(\sqrt{-64}\) and note that the number inside the square root (called the radicand) is negative.
4. Since the radicand is negative, \(\sqrt{-64}\) does not represent a real number; instead, it is an imaginary number in the complex number system.
5. Therefore, conclude that \(\sqrt{-64}\) is not a real number because the square root of a negative number is not defined in the set of real numbers.