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−−−√

Answer 1

To find an irrational number between 9 and 11, we can look at the square roots of numbers in that range.

1. The square root of 100 is 10, which is a rational number.
2. The square root of 99 is approximately 9.949874, which is an irrational number since 99 is not a perfect square.
3. The square root of 10 is approximately 3.16227766, which is also irrational but not in the range between 9 and 11.
4. The square root of 20 is approximately 4.47213595, which is irrational but again not in the specified range.

Thus, the best choice from the options given that is indeed an irrational number between 9 and 11 is:

\(\sqrt{99}\)

So, the answer is \(\sqrt{99}\).