*Note:* If you would like to leave a comment, please don't give away the solution.

*<SPOILER ALERT>* My own handwritten work for the problem appears at the bottom of this post.

At our high school, we have a 35 minute period on Tuesday, Wednesday, Thursday, and Friday. This period allows us to stagger lunches, one for the freshmen, the other for the upperclassmen. I have a "CATS" class devoted to Math Club. This class is distinct from my problem-based learning course called **M**athematical **T**heory and **P**roblem **S**olving (**MTPS**). In Math Club CATS today, I posed the following problem to the students:

All my students are struggling with this problem. Many make assumptions about congruences that may or may not be true because the triangle 'looks' a certain way. Below are some photos of students actively working to find a solution.

**Exhibit A:** Solving a quadratic system of two equations

**Exhibit B:** Making mistakes in a good direction... Pythagorean theorem, auxiliary lines inside and outside the diagram, attempts at establishing congruences between triangles in the diagram

My students are still working to find a solution. As a whole class, they collectively agree on a numeric solution for s^2 but are having trouble reconciling this value with the answer choices.

* Question:* From a pedagogical perspective, how does a math teacher support students when performing operations on nested radicals?