Question
What is a rational number square root of 93, square root of 23, square root of 16, square root of 54?
Answers
Answered by
GPT-4o mini
To determine if the square roots of the given numbers are rational or not, we need to consider each one separately:
1. **Square root of 93**:
- \(\sqrt{93}\) is not a perfect square. It cannot be expressed as a fraction of two integers, so it is an **irrational number**.
2. **Square root of 23**:
- \(\sqrt{23}\) is also not a perfect square. Like the previous case, it cannot be expressed as a fraction of two integers, making it an **irrational number**.
3. **Square root of 16**:
- \(\sqrt{16} = 4\), which is an integer and can be expressed as the fraction \(4/1\). Thus, it is a **rational number**.
4. **Square root of 54**:
- \(\sqrt{54} = \sqrt{9 \times 6} = 3\sqrt{6}\). Since \(\sqrt{6}\) is irrational, \(3\sqrt{6}\) is also irrational. Therefore, \(\sqrt{54}\) is an **irrational number**.
In summary:
- \(\sqrt{93}\): irrational
- \(\sqrt{23}\): irrational
- \(\sqrt{16}\): rational
- \(\sqrt{54}\): irrational
1. **Square root of 93**:
- \(\sqrt{93}\) is not a perfect square. It cannot be expressed as a fraction of two integers, so it is an **irrational number**.
2. **Square root of 23**:
- \(\sqrt{23}\) is also not a perfect square. Like the previous case, it cannot be expressed as a fraction of two integers, making it an **irrational number**.
3. **Square root of 16**:
- \(\sqrt{16} = 4\), which is an integer and can be expressed as the fraction \(4/1\). Thus, it is a **rational number**.
4. **Square root of 54**:
- \(\sqrt{54} = \sqrt{9 \times 6} = 3\sqrt{6}\). Since \(\sqrt{6}\) is irrational, \(3\sqrt{6}\) is also irrational. Therefore, \(\sqrt{54}\) is an **irrational number**.
In summary:
- \(\sqrt{93}\): irrational
- \(\sqrt{23}\): irrational
- \(\sqrt{16}\): rational
- \(\sqrt{54}\): irrational