Question

Classify each product or sum as rational or irrational.



Move the options to the spaces to correctly complete the table.

Response area with 6 blank spaces
Expression Rational or Irrational
3 plus StartRoot 9 EndRoot
Blank space 21 empty

StartRoot 2 EndRoot plus StartRoot 2 EndRoot
Blank space 22 empty

5 times pi
Blank space 23 empty

StartRoot 2 EndRoot times StartRoot 3 EndRoot
Blank space 24 empty

StartRoot 2 EndRoot times StartRoot 8 EndRoot
Blank space 25 empty

five-ninths times 0 point ModAbove 5 4 with Bar
Blank space 26 empty




Answer options with 2 options.

Answer 1

To classify each expression as rational or irrational, we'll evaluate them one by one:

1. **3 plus √9**
- √9 = 3, so the expression is 3 + 3 = 6.
- **Rational**

2. **√2 plus √2**
- This is 2√2, which is not a rational number.
- **Irrational**

3. **5 times π**
- π is an irrational number, so 5π is also irrational.
- **Irrational**

4. **√2 times √3**
- This equals √(2*3) = √6, which is irrational.
- **Irrational**

5. **√2 times √8**
- This equals √(2*8) = √16 = 4, which is rational.
- **Rational**

6. **five-ninths times 0.5 repeating**
- 0.5 repeating is equivalent to 1/3, so five-ninths (5/9) times (1/3) equals 5/27, which is rational.
- **Rational**

Now, let's fill in the table:

| Expression | Rational or Irrational |
|-------------------------------------------|------------------------|
| 3 plus √9 | Rational |
| √2 plus √2 | Irrational |
| 5 times π | Irrational |
| √2 times √3 | Irrational |
| √2 times √8 | Rational |
| five-ninths times 0.5 repeating | Rational |

So the filled responses should be:

- Blank space 21: Rational
- Blank space 22: Irrational
- Blank space 23: Irrational
- Blank space 24: Irrational
- Blank space 25: Rational
- Blank space 26: Rational