Problem

Study the following expressions and answer the questions that follow. a. (i) Prove that

\sqrt{12}

is an irrational number. b. (ii) Using the result of part (i), determine whether

3+\sqrt{12}

is rational or irrational. Provide a valid reason. c. (iii) Identify the smallest set among

\mathbb N,\;\mathbb W,\;\mathbb Z,\;\mathbb Q,\;\text{irrational numbers},\;\mathbb R

that contains the number

\dfrac{3+\sqrt{12}}{7}