Question
is negative square root of 5 irrational and square roof of 80
Answers
GPT-4o mini
Yes, both the negative square root of 5 and the square root of 80 can be classified in terms of rationality.
1. **Negative square root of 5 (\(-\sqrt{5}\))**:
- The square root of 5 is an irrational number because it cannot be expressed as a fraction of two integers. Therefore, its negative, \(-\sqrt{5}\), is also irrational.
2. **Square root of 80 (\(\sqrt{80}\))**:
- To simplify \(\sqrt{80}\), you can factor it as follows:
\[
\sqrt{80} = \sqrt{16 \times 5} = \sqrt{16} \times \sqrt{5} = 4\sqrt{5}
\]
- Since \(\sqrt{5}\) is irrational, \(4\sqrt{5}\) is also irrational (as the product of a rational number and an irrational number is irrational).
In summary, \(-\sqrt{5}\) and \(\sqrt{80}\) (which simplifies to \(4\sqrt{5}\)) are both irrational numbers.
1. **Negative square root of 5 (\(-\sqrt{5}\))**:
- The square root of 5 is an irrational number because it cannot be expressed as a fraction of two integers. Therefore, its negative, \(-\sqrt{5}\), is also irrational.
2. **Square root of 80 (\(\sqrt{80}\))**:
- To simplify \(\sqrt{80}\), you can factor it as follows:
\[
\sqrt{80} = \sqrt{16 \times 5} = \sqrt{16} \times \sqrt{5} = 4\sqrt{5}
\]
- Since \(\sqrt{5}\) is irrational, \(4\sqrt{5}\) is also irrational (as the product of a rational number and an irrational number is irrational).
In summary, \(-\sqrt{5}\) and \(\sqrt{80}\) (which simplifies to \(4\sqrt{5}\)) are both irrational numbers.