Determine the value of t:
$t^{2}=125$
Final Answer: The solutions to the equation \(t^{2}=125\) are \(t = \boxed{11.180339887498949}\) and \(t = \boxed{-11.180339887498949}\).
Step 1 :The question is asking for the value of t that satisfies the equation \(t^{2}=125\).
Step 2 :To solve for t, we need to take the square root of both sides of the equation.
Step 3 :However, we should remember that taking the square root of a number gives two possible solutions: a positive and a negative value.
Step 4 :The positive solution for t is \(\sqrt{125}\) which is approximately 11.180339887498949.
Step 5 :The negative solution for t is \(-\sqrt{125}\) which is approximately -11.180339887498949.
Step 6 :Final Answer: The solutions to the equation \(t^{2}=125\) are \(t = \boxed{11.180339887498949}\) and \(t = \boxed{-11.180339887498949}\).