Let's solve each expression one by one and determine if the result is a rational or irrational number.
-
0.5 + 3/4 \[ 0.5 = \frac{1}{2} \quad \text{and} \quad \frac{3}{4} = \frac{3}{4} \] Find a common denominator to add them: \[ \frac{1}{2} = \frac{2}{4} \quad \Rightarrow \quad \frac{2}{4} + \frac{3}{4} = \frac{5}{4} \] \(\frac{5}{4}\) is a rational number.
-
π + 3/4 \(\pi\) is an irrational number and \(\frac{3}{4}\) is a rational number. The sum of a rational number and an irrational number is always irrational. \(\pi + \frac{3}{4}\) is an irrational number.
-
√3 + 2/5 \(\sqrt{3}\) is an irrational number and \(\frac{2}{5}\) is a rational number. Similarly to the previous case, the sum of an irrational number and a rational number is irrational. \(\sqrt{3} + \frac{2}{5}\) is irrational.
-
√36 + 9 \(\sqrt{36} = 6\) (which is rational). Now add 9: \[ 6 + 9 = 15 \] \(15\) is a rational number.
-
1/9 + 5/2 Find a common denominator to add these fractions: The least common denominator of \(9\) and \(2\) is \(18\). \[ \frac{1}{9} = \frac{2}{18} \quad \text{and} \quad \frac{5}{2} = \frac{45}{18} \] Now add them: \[ \frac{2}{18} + \frac{45}{18} = \frac{47}{18} \] \(\frac{47}{18}\) is a rational number.
-
√4 + √4 \(\sqrt{4} = 2\) (which is rational). Now add: \[ 2 + 2 = 4 \] \(4\) is a rational number.
Summary:
- \(0.5 + \frac{3}{4} = \frac{5}{4}\) (rational)
- \(\pi + \frac{3}{4}\) (irrational)
- \(\sqrt{3} + \frac{2}{5}\) (irrational)
- \(\sqrt{36} + 9 = 15\) (rational)
- \(\frac{1}{9} + \frac{5}{2} = \frac{47}{18}\) (rational)
- \(\sqrt{4} + \sqrt{4} = 4\) (rational)