Show an example of an irrational number between 9 and 11.(1 point) Responses 20−−√ start root 20 end root 99−−√ start root 99 end root 10−−√ start root 10 end root 100−−−√

Answer 1

To find an irrational number between 9 and 11, we can consider the square roots of non-perfect squares within that range.

Let's evaluate the options:

1. \( \sqrt{20} \)

   • \( \sqrt{20} \approx 4.47 \) (not between 9 and 11)

2. \( \sqrt{99} \)

   • \( \sqrt{99} \approx 9.95 \) (which is between 9 and 11)

3. \( \sqrt{10} \)

   • \( \sqrt{10} \approx 3.16 \) (not between 9 and 11)

4. \( \sqrt{100} \)

   • \( \sqrt{100} = 10 \) (not an irrational number)

Among these options, \( \sqrt{99} \) is an irrational number that lies between 9 and 11.