Question
Which statements are true? Select the two correct answers.
The square root of a positive number greater than 1 is less than the number.
The square root of a positive number is always less than half of the number itself.
The square root of a positive number less than 1 is less than the number.
The square root of a perfect square is not a whole number.
The square root of a positive number less than 1 is between 0 and 1.
The square root of a positive number greater than 1 is less than the number.
The square root of a positive number is always less than half of the number itself.
The square root of a positive number less than 1 is less than the number.
The square root of a perfect square is not a whole number.
The square root of a positive number less than 1 is between 0 and 1.
Answers
GPT-4o mini
The two correct statements are:
1. **The square root of a positive number greater than 1 is less than the number.**
- This is true because if \( x > 1 \), then \( \sqrt{x} < x \).
2. **The square root of a positive number less than 1 is between 0 and 1.**
- This is also true because if \( 0 < x < 1 \), then \( \sqrt{x} \) will be greater than 0 but less than 1.
The other statements are false:
- **The square root of a positive number is always less than half of the number itself.** (This is not true for numbers greater than 4, for example.)
- **The square root of a perfect square is not a whole number.** (This is false since the square root of a perfect square is indeed a whole number.)
- **The square root of a positive number less than 1 is less than the number.** (This is true, but it is not one of the selected answers. The statement should be between 0 and 1 to be true.)
1. **The square root of a positive number greater than 1 is less than the number.**
- This is true because if \( x > 1 \), then \( \sqrt{x} < x \).
2. **The square root of a positive number less than 1 is between 0 and 1.**
- This is also true because if \( 0 < x < 1 \), then \( \sqrt{x} \) will be greater than 0 but less than 1.
The other statements are false:
- **The square root of a positive number is always less than half of the number itself.** (This is not true for numbers greater than 4, for example.)
- **The square root of a perfect square is not a whole number.** (This is false since the square root of a perfect square is indeed a whole number.)
- **The square root of a positive number less than 1 is less than the number.** (This is true, but it is not one of the selected answers. The statement should be between 0 and 1 to be true.)