Question

which equation results from taking the square root of both sides of ((x - 9)^2 = 81)?
\\(\bigcirc\\ x - 9 = \pm 9\\)
\\(\bigcirc\\ x + 9 = \pm 9\\)
\\(\bigcirc\\ x + 3 = \pm 9\\)
\\(\bigcirc\\ x - 3 = \pm 9\\)

Explanation:

Step1: Recall square root property

For an equation \(y^2 = a\) (where \(a\geq0\)), taking square root of both sides gives \(y=\pm\sqrt{a}\).
Here, let \(y = x - 9\) and \(a = 81\).

Step2: Apply the property

Take square root of both sides of \((x - 9)^2=81\).
Left side: \(\sqrt{(x - 9)^2}=|x - 9|\), but when solving equations like this, we can write \(x - 9=\pm\sqrt{81}\) (since if \((x - 9)^2 = 81\), then \(x - 9\) is a number whose square is 81, and such numbers are \(9\) and \(- 9\), so \(x - 9=\pm9\) as \(\sqrt{81}=9\)).

Answer:

A. \(x - 9=\pm9\)