Question

Show an example of an irrational number between 9 and 11.(1 point)
Responses

100−−−√
start root 100 end root

10−−√
start root 10 end root

20−−√
start root 20 end root

99−−√

What is the least integer whose square root is an irrational number between 5 and 7?(1 point)
Responses

26
26

25
25

6
6

13

Show an example of a rational number that is between 10−−√
and 11−−√
.(1 point)
Responses

3.1
3.1

165
Start Fraction 16 over 5 end fraction

3.4
3.4

10/3

Which irrational number is between 14−−√
and 18−−√
?(1 point)
Responses

15−−√
start root 15 end root

19−−√
start root 19 end root

10−−√
start root 10 end root

13−−√

How many irrational numbers are there between 11−−√
and 17−−√
?(1 point)
Responses

an infinite number
an infinite number

six numbers
six numbers

twenty-eight numbers
twenty-eight numbers

four numbers

Answer 1

Let's go through each question one by one.

1. **Show an example of an irrational number between 9 and 11.**
- The possible options include:
- \( \sqrt{100} = 10 \) (rational)
- \( \sqrt{10} \approx 3.16 \) (not between 9 and 11)
- \( \sqrt{20} \approx 4.47 \) (not between 9 and 11)
- \( \sqrt{99} \approx 9.95 \) (irrational)
- **Answer:** \( \sqrt{99} \)

2. **What is the least integer whose square root is an irrational number between 5 and 7?**
- The square roots we are considering:
- \( 5^2 = 25 \)
- \( 7^2 = 49 \)
- The least integer greater than 25 whose square root is irrational and less than 49 is 26.
- **Answer:** 26

3. **Show an example of a rational number that is between \( \sqrt{10} \) and \( \sqrt{11} \).**
- We know:
- \( \sqrt{10} \approx 3.16 \)
- \( \sqrt{11} \approx 3.32 \)
- A rational number between these two is \( \frac{16}{5} = 3.2 \).
- **Answer:** \( \frac{16}{5} \)

4. **Which irrational number is between \( \sqrt{14} \) and \( \sqrt{18} \)?**
- We know:
- \( \sqrt{14} \approx 3.74 \)
- \( \sqrt{18} \approx 4.24 \)
- An irrational number between these two is \( \sqrt{15} \).
- **Answer:** \( \sqrt{15} \)

5. **How many irrational numbers are there between \( \sqrt{11} \) and \( \sqrt{17} \)?**
- Since between any two real numbers (including square roots), there are infinitely many numbers, including both rational and irrational.
- **Answer:** an infinite number

Please let me know if you need further assistance!