1.1 Consider the given numbers: $$ \sqrt{32}, \sqrt[5]{32}, \sqrt{-32} $$. State which ONE of the following is:- 1.1.1 Irrational 1.1.2 Non-real 1.2 Show that 0,45 is a rational number.

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Let's analyze the given numbers step by step.

### 1.1 Given Numbers: $$ \sqrt{32}, \sqrt[5]{32}, \sqrt{-32} $$

#### 1.1.1 Identify the Irrational Number
- **$$ \sqrt{32} $$**: This can be simplified to $$ \sqrt{16 \cdot 2} = 4\sqrt{2} $$. Since $$ \sqrt{2} $$ is an irrational number, $$ \sqrt{32} $$ is also irrational.
- **$$ \sqrt[5]{32} $$**: This is equal to $$ 2 $$ because $$ 32 = 2^5 $$. Since $$ 2 $$ is a rational number, $$ \sqrt[5]{32} $$ is rational.
- **$$ \sqrt{-32} $$**: This is a non-real number because the square root of a negative number is not defined in the set of real numbers.

**Conclusion for 1.1.1**: The irrational number is $$ \sqrt{32} $$.

#### 1.1.2 Identify the Non-real Number
From the analysis above, the non-real number is $$ \sqrt{-32} $$.

### 1.2 Show that 0.45 is a Rational Number
A number is considered rational if it can be expressed as the quotient of two integers $$ \frac{a}{b} $$, where $$ b \neq 0 $$.

To express $$ 0.45 $$ as a fraction:
1. Write $$ 0.45 $$ as $$ \frac{45}{100} $$.
2. Simplify $$ \frac{45}{100} $$ by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is $$ 5 $$:
   $$
   \frac{45 \div 5}{100 \div 5} = \frac{9}{20}
   $$

Since $$ \frac{9}{20} $$ is a fraction where both $$ 9 $$ and $$ 20 $$ are integers and $$ 20 \neq 0 $$, $$ 0.45 $$ is a rational number.

**Conclusion for 1.2**: $$ 0.45 $$ is a rational number because it can be expressed as $$ \frac{9}{20} $$.
1.1.1 $$ \sqrt{32} $$ is irrational. 1.1.2 $$ \sqrt{-32} $$ is non-real. 1.2 $$ 0.45 $$ is a rational number because it can be expressed as $$ \frac{9}{20} $$.

1.1 Consider the given numbers: \( \sqrt{32}, \sqrt[5]{32}, \sqrt{-32} \). State which ONE of the following is:- 1.1.1 Irrational 1.1.2 Non-real 1.2 Show that 0,45 is a rational number.

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