Question

Solve and determine whether the result is a rational or irrational number.

0.5 + 3/4
Pi + 3/4
√3 + 2/5
√36 + 9
1/9 + 5/2
√4 + √4

Answer 1

Let's solve each expression one by one and determine if the result is a rational or irrational number.

1. **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.

2. **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. **√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.

4. **√36 + 9**
\(\sqrt{36} = 6\) (which is rational). Now add 9:
\[
6 + 9 = 15
\]
\(15\) is a rational number.

5. **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.

6. **√4 + √4**
\(\sqrt{4} = 2\) (which is rational).
Now add:
\[
2 + 2 = 4
\]
\(4\) is a rational number.

**Summary:**
1. \(0.5 + \frac{3}{4} = \frac{5}{4}\) (rational)
2. \(\pi + \frac{3}{4}\) (irrational)
3. \(\sqrt{3} + \frac{2}{5}\) (irrational)
4. \(\sqrt{36} + 9 = 15\) (rational)
5. \(\frac{1}{9} + \frac{5}{2} = \frac{47}{18}\) (rational)
6. \(\sqrt{4} + \sqrt{4} = 4\) (rational)