Please include steps clearly! Will upvote thanks!

2. Use a proof by contradiction to show that: is an irrational number To complete this proof you may use algebra, the logical equivalences, the inference rules, and the following additional "rules": the closure of rational numbers under multiplication" the product when two rational numbers are multiplied is a rational number "the definition of even numbers" x is an even number if and only if x can be written as 2k for some integer k "the definition of odd numbers" x is an odd number if and only if x can be written as 2k + 1 for some integer k "the definition of rational numbers x is a rational if and only ifit can be written as fraction x -in lowest form le, x A is in lowest form "lemma 1 (from class)" x2 being divisible by 2 x is also divisible by 2 "lemma 2 (from class)" xy is an even number A x is an odd number>y is an even number You may not use any rules other than those mentioned above. You must show every step, and every step must be numbered and labelled (with whatever you "used" for that step of the proof). Complete your proof on the following page [10 marks]