Question

which equation results from taking the square root of both sides of ((x + 9)^2 = 25)?
(x + 3 = pm5)
(x + 3 = pm25)
(x + 9 = pm5)
(x + 9 = pm25)

Explanation:

Step1: Recall square root property

When we take the square root of both sides of an equation of the form \(y^{2}=a\) (where \(a\geq0\)), we get \(y = \pm\sqrt{a}\).

Step2: Apply to given equation

Given the equation \((x + 9)^{2}=25\). Let \(y=x + 9\) and \(a = 25\). Taking the square root of both sides, we have \(x+9=\pm\sqrt{25}\). Since \(\sqrt{25}=5\), this simplifies to \(x + 9=\pm5\).

Answer:

C. \(x + 9=\pm5\) (assuming the options are labeled A, B, C, D with C being \(x + 9=\pm5\))