# Question: 6 prove p7 is irrational using the fundamental theorem of...

###### Question details

6. Prove p7 is irrational using the Fundamental Theorem of
Arithmetic by carrying out the following steps: p p

Use a proof by contradiction. Suppose 7 is rational. This
implies 7 = a/b for some integers a and b. You can assume that a
and b are both positive (explain why). Then a2 = 7b2. Use the
Fundamental Theorem to write prime factorizations for a and b and
show that you get a contradiction after you substitute into the
equation a2 = 7b2.