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.