Question: Let a and b be real numbers, with a < b. Complete parts (i) and (ii) below: (i) Show that there is a rational number

Let a and b be real numbers, with a < b. Complete parts (i) and (ii) below:

(i) Show that there is a rational number r, such that a < r2 < b

(ii) Now, show by contradiction that r2 is irrational. Thereby providing that between any two real numbers, there is at least one irrational number.

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