Numbers Between Rational Numbers Quick Check

Question

3 of 53 of 5 Items
Question
Show an example of a rational number that is between 10−−√ and 11−−√.(1 point)
Responses

165
Start Fraction 16 over 5 end fraction

3.1
3.1

103
Start Fraction 10 over 3 end fraction

3.4

Answer 1

To find a rational number between \( \sqrt{10} \) and \( \sqrt{11} \), we start by calculating approximate values for these square roots:

• \( \sqrt{10} \approx 3.162 \)
• \( \sqrt{11} \approx 3.317 \)

A rational number between these two values should be greater than \( \sqrt{10} \) and less than \( \sqrt{11} \).

Now, let's analyze the given options:

1. \( \frac{16}{5} = 3.2 \) (this is between \( \sqrt{10} \) and \( \sqrt{11} \))
2. \( 3.1 \) (this is between \( \sqrt{10} \) and \( \sqrt{11} \))
3. \( \frac{10}{3} \approx 3.333 \) (this is not between \( \sqrt{10} \) and \( \sqrt{11} \))
4. \( 3.4 \) (this is not between \( \sqrt{10} \) and \( \sqrt{11} \))

So, valid rational numbers from the options given that are between \( \sqrt{10} \) and \( \sqrt{11} \) are:

• \( \frac{16}{5} \)
• \( 3.1 \)

Either of these responses would be correct. However, since you need to show an example, \( \frac{16}{5} \) or \( 3.1 \) are valid examples of rational numbers between \( \sqrt{10} \) and \( \sqrt{11} \).