Question
which is a rational number
37/25 pi √40 √54
37/25 pi √40 √54
Answers
GPT-4o mini
A rational number is defined as a number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero.
Let's analyze the given numbers:
1. **\( \frac{37}{25} \)**: This is a fraction and can be expressed as the ratio of two integers. Therefore, it is a rational number.
2. **\( \pi \)**: This is an irrational number, as it cannot be expressed as a fraction of two integers.
3. **\( \sqrt{40} \)**: This can be simplified to \( \sqrt{4 \times 10} = 2\sqrt{10} \). Since \( \sqrt{10} \) is irrational, \( \sqrt{40} \) is also irrational.
4. **\( \sqrt{54} \)**: This can be simplified to \( \sqrt{9 \times 6} = 3\sqrt{6} \). Since \( \sqrt{6} \) is irrational, \( \sqrt{54} \) is also irrational.
In summary, among the numbers you provided, the only rational number is \( \frac{37}{25} \).
Let's analyze the given numbers:
1. **\( \frac{37}{25} \)**: This is a fraction and can be expressed as the ratio of two integers. Therefore, it is a rational number.
2. **\( \pi \)**: This is an irrational number, as it cannot be expressed as a fraction of two integers.
3. **\( \sqrt{40} \)**: This can be simplified to \( \sqrt{4 \times 10} = 2\sqrt{10} \). Since \( \sqrt{10} \) is irrational, \( \sqrt{40} \) is also irrational.
4. **\( \sqrt{54} \)**: This can be simplified to \( \sqrt{9 \times 6} = 3\sqrt{6} \). Since \( \sqrt{6} \) is irrational, \( \sqrt{54} \) is also irrational.
In summary, among the numbers you provided, the only rational number is \( \frac{37}{25} \).