Question

what is the radius of the circle $x^2 + y^2 = 144$?
write your answer in simplified, rationalized form.

Explanation:

Step1: Recall circle equation form

The standard form of a circle's equation is \((x - h)^2 + (y - k)^2 = r^2\), where \((h,k)\) is the center and \(r\) is the radius.

Step2: Compare with given equation

The given equation is \(x^2 + y^2 = 144\), which can be written as \((x - 0)^2 + (y - 0)^2 = 12^2\) (since \(144 = 12\times12\)). By comparing with the standard form, we see that \(r^2 = 144\).

Step3: Solve for radius \(r\)

To find \(r\), we take the square root of both sides: \(r=\sqrt{144}\). Since the radius is a non - negative quantity, \(r = 12\).

Answer:

12