Question 3

We will use the definition of irrational numbers to describe $\sqrt{17}$.

Step 1 — Recall definitions

We know what an irrational number is. Its decimal expansion is special. It is non-terminating. This means it never ends. It is also non-recurring. This means no digits repeat in a pattern.

We are given that $\sqrt{17}$ is irrational. This is a key piece of information.

Step 2 — Conclude about $\sqrt{17}$

Let's combine these facts. We know $\sqrt{17}$ is an irrational number. We also know irrational numbers have specific properties. Their decimal expansions are non-terminating. Their decimal expansions are non-recurring. Therefore, $\sqrt{17}$ must have these properties.

$\text{If a number is irrational} \implies \text{Its decimal expansion is non-terminating}$ $\text{If a number is irrational} \implies \text{Its decimal expansion is non-recurring}$ $\text{Given that } \sqrt{17} \text{ is irrational}$

$\boxed{\text{The decimal expansion of } \sqrt{17} \text{ is non-terminating and non-recurring.}}$

Answer

(i) The decimal expansion of $\sqrt{17}$ is non-terminating. (ii) The decimal expansion of $\sqrt{17}$ is non-recurring.