Question

Which numbers are rational? Check the three that apply.(3 points)
Responses

32−−√
square root of 32

4.52525252...

1217
12 over 17

70−−√
square root of 70

16−−√
square root of 16

π

Answer 1

To determine which of the given numbers are rational, we need to remember that a rational number can be expressed as the quotient of two integers (i.e., as a fraction).

Let's evaluate each option:

1. **√32** (square root of 32) - This is not a rational number, as it cannot be expressed as a fraction of two integers (it is approximately 5.657).

2. **4.52525252...** - This is a repeating decimal, which can be expressed as a fraction (specifically, 4.52... is rational).

3. **12/17** - This is a fraction where both numerator and denominator are integers, so it is a rational number.

4. **√70** (square root of 70) - Similar to √32, this is not a rational number (approximately 8.366).

5. **√16** (square root of 16) - This equals 4, which is a whole number and can be expressed as 4/1, so it is rational.

6. **π** - This is an irrational number, as it cannot be expressed as a fraction of two integers.

Based on this evaluation, the rational numbers among the options given are:

- **4.52525252...**
- **12/17**
- **√16**

So the three numbers that are rational are **4.52525252..., 12/17, and √16**.