Question
-0.0123456...
square root of 15
0
7/3
square root of -45
3 square root of 27
answer correctly
square root of 15
0
7/3
square root of -45
3 square root of 27
answer correctly
Answers
Answer
rearrange them from largest to smallest
Answered by
GPT-4o mini
Here's the evaluation of each expression you provided:
1. **-0.0123456...**: This number can be interpreted as a repeating decimal, which is approximately \(-0.0123456\).
2. **Square root of 15**: The square root of 15 is an irrational number and is approximately \(3.872983\).
3. **0**: This is simply \(0\).
4. **7/3**: The fraction \(7/3\) is approximately \(2.3333\).
5. **Square root of -45**: The square root of -45 is an imaginary number since the square root of a negative number is not defined in the set of real numbers. It can be expressed as:
\[
\sqrt{-45} = \sqrt{45} \cdot i = 3\sqrt{5} \cdot i \approx 6.7082i
\]
6. **3 times the square root of 27**: The square root of 27 can be simplified:
\[
\sqrt{27} = \sqrt{9 \cdot 3} = 3\sqrt{3}
\]
Therefore,
\[
3 \cdot \sqrt{27} = 3 \cdot 3\sqrt{3} = 9\sqrt{3} \approx 15.5885.
\]
So, summarizing the answers:
1. \(-0.0123456...\)
2. \(\sqrt{15} \approx 3.872983\)
3. \(0\)
4. \(7/3 \approx 2.3333\)
5. \(3\sqrt{5}i \approx 6.7082i\)
6. \(9\sqrt{3} \approx 15.5885\)
1. **-0.0123456...**: This number can be interpreted as a repeating decimal, which is approximately \(-0.0123456\).
2. **Square root of 15**: The square root of 15 is an irrational number and is approximately \(3.872983\).
3. **0**: This is simply \(0\).
4. **7/3**: The fraction \(7/3\) is approximately \(2.3333\).
5. **Square root of -45**: The square root of -45 is an imaginary number since the square root of a negative number is not defined in the set of real numbers. It can be expressed as:
\[
\sqrt{-45} = \sqrt{45} \cdot i = 3\sqrt{5} \cdot i \approx 6.7082i
\]
6. **3 times the square root of 27**: The square root of 27 can be simplified:
\[
\sqrt{27} = \sqrt{9 \cdot 3} = 3\sqrt{3}
\]
Therefore,
\[
3 \cdot \sqrt{27} = 3 \cdot 3\sqrt{3} = 9\sqrt{3} \approx 15.5885.
\]
So, summarizing the answers:
1. \(-0.0123456...\)
2. \(\sqrt{15} \approx 3.872983\)
3. \(0\)
4. \(7/3 \approx 2.3333\)
5. \(3\sqrt{5}i \approx 6.7082i\)
6. \(9\sqrt{3} \approx 15.5885\)
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