To solve the equation \( t^2 = 50 \):

1. Take the square root of both sides of the equation to solve for \( t \):
   \[
   t = \pm \sqrt{50}
   \]

2. Simplify \( \sqrt{50} \):
   \[
   \sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2}
   \]

Therefore, the solution is:
\[
t = \pm 5\sqrt{2}
\]

This means \( t \) can be either \( 5\sqrt{2} \) or \( -5\sqrt{2} \).

Would you like further details, or do you have any questions?

Here are some related questions:
1. What are the properties of square roots in equations?
2. How do you rationalize square roots in denominators?
3. How do you solve quadratic equations with complex numbers?
4. What is the geometric interpretation of square roots?
5. How do you simplify expressions with nested square roots?

**Tip:** When simplifying square roots, always check if the number under the root has any perfect square factors.

Learn how to solve the equation t^2 = 50 with a step-by-step solution. This problem covers equations involving square roots and simplification of radicals. Suitable for students in Grades 9-12.

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