4. Use a proof by contradiction to show that the square root of3 is irrational. You may use the following fact: For any integer k,if k2 is a multiple of 3, then k is a multiple of 3. Hint: Theproof is very similar to the proof that ?2 is irrational.
5. Use a direct proof to show that the product of a rationalnumber and an integer must be a rational number.
6. Use a proof by contradiction to show that the sum of aninteger and an irrational number must be irrational.
