Question

Which expression represents a rational number?
StartFraction 5 Over 9 EndFraction + StartRoot 18 EndRoot
Pi + StartRoot 16 EndRoot
StartFraction 2 Over 7 EndFraction + StartRoot 121 EndRoot
StartFraction 3 Over 10 EndFraction + StartRoot 11 EndRoot

Answer 1

To determine which of the given expressions represents a rational number, we need to identify whether each individual term in the expressions is rational or irrational.

1. **Expression: \( \frac{5}{9} + \sqrt{18} \)**
- \( \frac{5}{9} \) is a rational number.
- \( \sqrt{18} = \sqrt{9 \cdot 2} = 3\sqrt{2} \), which is irrational.
- Therefore, \( \frac{5}{9} + \sqrt{18} \) is irrational.

2. **Expression: \( \pi + \sqrt{16} \)**
- \( \pi \) is an irrational number.
- \( \sqrt{16} = 4 \), which is rational.
- Therefore, \( \pi + \sqrt{16} \) is irrational.

3. **Expression: \( \frac{2}{7} + \sqrt{121} \)**
- \( \frac{2}{7} \) is a rational number.
- \( \sqrt{121} = 11 \), which is also rational.
- Therefore, \( \frac{2}{7} + \sqrt{121} = \frac{2}{7} + 11 \), which is rational.

4. **Expression: \( \frac{3}{10} + \sqrt{11} \)**
- \( \frac{3}{10} \) is a rational number.
- \( \sqrt{11} \) is irrational.
- Therefore, \( \frac{3}{10} + \sqrt{11} \) is irrational.

From these evaluations, the only expression that represents a rational number is:

\[
\frac{2}{7} + \sqrt{121}
\]