Question

solve the equation by the square root property.
$(x - 8)^2 = 5$
a. ${\sqrt{5} - 8, -\sqrt{5} - 8}$
b. ${\sqrt{5} - \sqrt{-8}}$
c. ${8 \pm \sqrt{5}}$
d. ${8 + \sqrt{5}}$

Explanation:

Step1: Apply square root property

The square root property states that if \(u^2 = v\), then \(u=\pm\sqrt{v}\). For the equation \((x - 8)^2=5\), let \(u = x - 8\) and \(v = 5\). So we have \(x - 8=\pm\sqrt{5}\).

Step2: Solve for x

To solve for \(x\), we add 8 to both sides of the equation \(x - 8=\pm\sqrt{5}\). This gives us \(x=8\pm\sqrt{5}\). So the solution set is \(\{8\pm\sqrt{5}\}\).

Answer:

C. \(\{8\pm\sqrt{5}\}\)