$$ \text { Practise Questions } \frac{17 / 03 / 25}{} $$ (1) $$ \sqrt{18} ; \pi ;-\sqrt{\frac{16}{9}} ; 0,17 ; 0, i 7 ; 1+16 ; \frac{26}{13} ; \frac{5}{0} ; 3 $$ a) Which number are undefined b) non-real c) irrational

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Let's analyze the given numbers step by step to identify which ones are undefined, non-real, and irrational.

The numbers provided are:
1. $$ \sqrt{18} $$
2. $$ \pi $$
3. $$ -\sqrt{\frac{16}{9}} $$
4. $$ 0.17 $$
5. $$ 0 $$
6. $$ i $$
7. $$ 7 $$
8. $$ 1 + 16 $$
9. $$ \frac{26}{13} $$
10. $$ \frac{5}{0} $$
11. $$ 3 $$

### a) Undefined Numbers
A number is considered undefined if it involves division by zero. In this case, the only number that fits this criterion is:
- $$ \frac{5}{0} $$

### b) Non-Real Numbers
Non-real numbers include imaginary numbers. The only non-real number in the list is:
- $$ i $$ (the imaginary unit)

### c) Irrational Numbers
Irrational numbers cannot be expressed as a fraction of two integers. Let's evaluate each number:
1. $$ \sqrt{18} $$ is irrational because it cannot be simplified to a fraction.
2. $$ \pi $$ is known to be irrational.
3. $$ -\sqrt{\frac{16}{9}} = -\frac{4}{3} $$ is rational.
4. $$ 0.17 $$ is rational.
5. $$ 0 $$ is rational.
6. $$ i $$ is not a real number, so it is not classified as rational or irrational.
7. $$ 7 $$ is rational.
8. $$ 1 + 16 = 17 $$ is rational.
9. $$ \frac{26}{13} = 2 $$ is rational.
10. $$ \frac{5}{0} $$ is undefined.
11. $$ 3 $$ is rational.

Thus, the irrational numbers are:
- $$ \sqrt{18} $$
- $$ \pi $$

### Summary of Results
- **Undefined Numbers:** $$ \frac{5}{0} $$
- **Non-Real Numbers:** $$ i $$
- **Irrational Numbers:** $$ \sqrt{18}, \pi $$
- **Undefined Numbers:** $$ \frac{5}{0} $$ - **Non-Real Numbers:** $$ i $$ - **Irrational Numbers:** $$ \sqrt{18}, \pi $$

\[ \text { Practise Questions } \frac{17 / 03 / 25}{} \] (1) \( \sqrt{18} ; \pi ;-\sqrt{\frac{16}{9}} ; 0,17 ; 0, i 7 ; 1+16 ; \frac{26}{13} ; \frac{5}{0} ; 3 \) a) Which number are undefined b) non-real c) irrational

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