Study the following expressions and answer the questions that follow.

MATHEMATICS · Multi-part · CBSE · Mathematics · Number Systems · Number Systems

Problem

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

\sqrt{12}

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

3+\sqrt{12}

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

\mathbb{N}

\mathbb{W}

\mathbb{Z}

\mathbb{Q}

, irrational numbers, and

\mathbb{R}

that contains the number

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