To determine which of the following numbers is not a real number, we need to evaluate each given square root:
A. [tex]\(\sqrt{5}\)[/tex]: This is the square root of a positive number, which always results in a real number. For [tex]\(\sqrt{5}\)[/tex], the result is approximately 2.236.
B. [tex]\(\sqrt{-3}\)[/tex]: This is the square root of a negative number. In the set of real numbers, the square root of a negative number does not exist because there is no real number that, when squared, gives a negative result. Therefore, [tex]\(\sqrt{-3}\)[/tex] is not a real number.
C. [tex]\(\sqrt{4}\)[/tex]: The square root of 4 is a real number. Specifically, [tex]\(\sqrt{4} = 2\)[/tex], since [tex]\(2 \times 2 = 4\)[/tex].
D. [tex]\(\sqrt{0}\)[/tex]: The square root of 0 is also a real number. Specifically, [tex]\(\sqrt{0} = 0\)[/tex], as [tex]\(0 \times 0 = 0\)[/tex].
Thus, among the given options, [tex]\(\sqrt{-3}\)[/tex] is the only one that is not a real number. Therefore, the correct answer is:
B. [tex]\(\sqrt{-3}\)[/tex]
