Question

simplify
\\(\sqrt{(-1)^2}\\)
select the correct choice below and, if necessary, fill in the answer box that completes your choice.
\\(\bigcirc\\) a. \\(\sqrt{(-1)^2} = \square\\)
(type an exact answer, using radicals as needed.)
\\(\bigcirc\\) b. the square root is not a real number

Explanation:

Step1: Simplify the expression inside the square root

First, we calculate \((-1)^2\). By the definition of squaring a number, \((-1)^2 = (-1) \times (-1) = 1\).

Step2: Take the square root of the result

Now we need to find \(\sqrt{1}\). The square root of a number \(x\) is a number \(y\) such that \(y^2 = x\). For \(x = 1\), we know that \(1^2 = 1\) and \((-1)^2 = 1\), but when we talk about the principal square root (the non - negative square root), \(\sqrt{1}=1\).

Answer:

A. \(\sqrt{(-1)^{2}}=\boxed{1}\)