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 for \(a \geq 0\) because the square of any real number is non-negative.
3. Look at the given expression: \(\sqrt{-64}\). Here, the number inside the square root (called the radicand) is \(-64\), which is less than zero.
4. Since the radicand is negative, there is no real number that, when squared, equals \(-64\). This means \(\sqrt{-64}\) is not a real number.
5. Therefore, the square root of \(-64\) does not evaluate to a real number; it is considered 'Not Real' in the context of real numbers.