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.

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 \( \frac{9}{20} \).