Question
determines if each number is rational or irrational
0
-√9
5/4
^3√25
-√2
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2
0
-√9
5/4
^3√25
-√2
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2
Answers
GPT-4o mini
Let's evaluate each number in your list to determine if it is rational or irrational.
1. **0**: This is a rational number because it can be expressed as the fraction \(0/1\).
2. **-√9**: The expression simplifies to \(-3\) (since \(\sqrt{9} = 3\)). This is also a rational number because it can be expressed as \(-3/1\).
3. **5/4**: This is a rational number because it is already in the form of a fraction (where both the numerator and denominator are integers and the denominator is not zero).
4. **^3√25**: The cube root of 25 (\(\sqrt[3]{25}\)) is approximately 2.924, which is not a precise fraction of integers. Therefore, this number is irrational.
5. **-√2**: The square root of 2 is known to be an irrational number, and since -√2 is just the negative of an irrational number, it is also irrational.
So, to summarize:
- 0: Rational
- -√9: Rational
- 5/4: Rational
- ^3√25: Irrational
- -√2: Irrational
1. **0**: This is a rational number because it can be expressed as the fraction \(0/1\).
2. **-√9**: The expression simplifies to \(-3\) (since \(\sqrt{9} = 3\)). This is also a rational number because it can be expressed as \(-3/1\).
3. **5/4**: This is a rational number because it is already in the form of a fraction (where both the numerator and denominator are integers and the denominator is not zero).
4. **^3√25**: The cube root of 25 (\(\sqrt[3]{25}\)) is approximately 2.924, which is not a precise fraction of integers. Therefore, this number is irrational.
5. **-√2**: The square root of 2 is known to be an irrational number, and since -√2 is just the negative of an irrational number, it is also irrational.
So, to summarize:
- 0: Rational
- -√9: Rational
- 5/4: Rational
- ^3√25: Irrational
- -√2: Irrational