Question

Which expressions represent rational numbers? Check all that apply.
StartRoot 6 EndRoot + StartRoot 9 EndRoot
StartRoot 64 EndRoot + StartFraction 6 Over 11 EndFraction
StartRoot 36 EndRoot + StartRoot 21 EndRoot
StartRoot 16 EndRoot + StartRoot 169 EndRoot
17.ModifyingAbove 43 with bar + StartRoot 49 EndRoot
StartRoot 44 EndRoot + StartRoot 25 EndRoot

Answer 1

To determine which expressions represent rational numbers, we need to evaluate each expression and check if they result in a rational number (a number that can be expressed as a fraction of two integers).

1. **StartRoot 6 EndRoot + StartRoot 9 EndRoot**
\( \sqrt{6} + \sqrt{9} = \sqrt{6} + 3 \)
This expression is not a rational number because \( \sqrt{6} \) is irrational.

2. **StartRoot 64 EndRoot + StartFraction 6 Over 11 EndFraction**
\( \sqrt{64} + \frac{6}{11} = 8 + \frac{6}{11} \)
This is a rational number because both 8 and \( \frac{6}{11} \) are rational.

3. **StartRoot 36 EndRoot + StartRoot 21 EndRoot**
\( \sqrt{36} + \sqrt{21} = 6 + \sqrt{21} \)
This expression is not a rational number because \( \sqrt{21} \) is irrational.

4. **StartRoot 16 EndRoot + StartRoot 169 EndRoot**
\( \sqrt{16} + \sqrt{169} = 4 + 13 \)
This is a rational number because both 4 and 13 are rational, and their sum (17) is also rational.

5. **17.ModifyingAbove 43 with bar + StartRoot 49 EndRoot**
\( 17.\overline{43} + \sqrt{49} = 17.\overline{43} + 7 \)
The repeating decimal \( 17.\overline{43} \) is a rational number, and adding 7 (which is also rational) results in a rational number.

6. **StartRoot 44 EndRoot + StartRoot 25 EndRoot**
\( \sqrt{44} + \sqrt{25} = \sqrt{44} + 5 \)
This expression is not a rational number because \( \sqrt{44} \) is irrational.

Based on this analysis, the expressions that represent rational numbers are:

- **StartRoot 64 EndRoot + StartFraction 6 Over 11 EndFraction**
- **StartRoot 16 EndRoot + StartRoot 169 EndRoot**
- **17.ModifyingAbove 43 with bar + StartRoot 49 EndRoot**