Determine the value of t: $t^{2}=125$

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 \(t = \boxed{-11.180339887498949}\).