Question

question 9 of 10
which of the following is not a real number?

a. \\(\sqrt{-4}\\)

b. \\(\sqrt{1}\\)

c. \\(\sqrt{13}\\)

d. \\(\sqrt{16}\\)

Explanation:

Step1: Recall real number definition for square roots

The square root of a negative number is not a real number (it's an imaginary number). For non - negative numbers \(a\), \(\sqrt{a}\) is a real number if \(a\geq0\).

Step2: Analyze each option

• Option A: For \(\sqrt{- 4}\), the number inside the square root (\(-4\)) is negative. By the definition of square roots in real numbers, \(\sqrt{-4}\) is not a real number (it can be written as \(2i\) where \(i\) is the imaginary unit, \(i = \sqrt{-1}\)).
• Option B: For \(\sqrt{1}\), since \(1\geq0\), \(\sqrt{1}=1\), which is a real number.
• Option C: For \(\sqrt{13}\), since \(13\geq0\), \(\sqrt{13}\) is a real number (it is an irrational real number).
• Option D: For \(\sqrt{16}\), since \(16\geq0\), \(\sqrt{16} = 4\), which is a real number.

Answer:

A. \(\boldsymbol{\sqrt{-4}}\)