Question
.Show an example of an irrational number between 9 and 11.(1 point)
Responses
99−−√
start root 99 end root
10−−√
start root 10 end root
20−−√
start root 20 end root
100−−−√
Responses
99−−√
start root 99 end root
10−−√
start root 10 end root
20−−√
start root 20 end root
100−−−√
Answers
GPT-4o mini
An example of an irrational number between 9 and 11 is \(\sqrt{99}\).
Just to clarify:
- \(\sqrt{99}\) is approximately 9.95, which lies between 9 and 11.
- \(\sqrt{10}\) is approximately 3.16, which does not fit the range.
- \(\sqrt{20}\) is approximately 4.47, which also does not fit the range.
- \(\sqrt{100}\) is 10, which is rational.
Therefore, the best choice for an irrational number between 9 and 11 is \(\sqrt{99}\).
Just to clarify:
- \(\sqrt{99}\) is approximately 9.95, which lies between 9 and 11.
- \(\sqrt{10}\) is approximately 3.16, which does not fit the range.
- \(\sqrt{20}\) is approximately 4.47, which also does not fit the range.
- \(\sqrt{100}\) is 10, which is rational.
Therefore, the best choice for an irrational number between 9 and 11 is \(\sqrt{99}\).