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MATH 131A Week 2 Group Worksheet

January 16, 2024

Instructions: You are encouraged to work on these problems with your assigned group. At the end of discussion, each group should submit a single sheet with clean, well-justified proofs for each problem.

Problem 1.

(a) Show that  is not a rational number.

(b) Show that  is not a rational number.

(c) Show that  is a rational number (Hint: set  and consider pa .)

Problem 2. Show that  for all a, b ∈ R.

Problem 3. [Nested Expressions] Evaluate the following expressions.

How are you able to exclude the extraneous roots of these expressions? Can you rigorously explain what each expression means? We will discuss this later in the course.