Question

Square root of 101
0.424242424...
square root of 16
0.133134135...
0.789

irrational because the decimal is non-terminating, non-repeating
rational because it is the square root of a perfect square
rational because the decimal does not terminate
rational because the decimal repeats
irrational because it is the square root of a non-perfect square
irrational because the decimal repeats
rational because the decimal terminates

Answer 1

Let's analyze the numbers you've provided and determine whether they are rational or irrational:

1. **Square root of 101**:
- Decimal form: Approximately 10.04987562...
- Classification: **Irrational** because it is the square root of a non-perfect square (101 is not a perfect square).

2. **0.424242424...**:
- This is a repeating decimal (0.42 repeats indefinitely).
- Classification: **Rational** because it can be expressed as a fraction (e.g., 42/99).

3. **Square root of 16**:
- Decimal form: 4
- Classification: **Rational** because it is the square root of a perfect square (16 is a perfect square).

4. **0.133134135...**:
- This appears not to be repeating, resulting in a non-terminating decimal.
- Classification: **Irrational**, assuming it doesn't have a repeating pattern, as it's not expressed as a fraction.

5. **0.789**:
- Decimal form: 0.789 (terminates)
- Classification: **Rational** because the decimal terminates.

**Summary**:
- Square root of 101: Irrational
- 0.424242424...: Rational
- Square root of 16: Rational
- 0.133134135...: Irrational
- 0.789: Rational

Thus, the classifications are as follows:
1. Irrational (sqrt(101) -> non-perfect square)
2. Rational (0.4242... -> repeating decimal)
3. Rational (sqrt(16) -> perfect square)
4. Irrational (0.133134135... -> non-terminating, presumed non-repeating)
5. Rational (0.789 -> terminating decimal)