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