Question

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

10

660

<

20

100

Answer 1

An example of an irrational number between 9 and 11 is \(10 + \sqrt{2}\). The value of \(\sqrt{2}\) is approximately 1.414, so:

\[
10 + \sqrt{2} \approx 10 + 1.414 = 11.414
\]

However, since we want a number specifically between 9 and 11, we can try a number like \(9.5 + \sqrt{0.25}\), which is irrational:

\[
9.5 + \sqrt{0.5} \approx 9.5 + 0.707 = 10.207
\]

This is an irrational number between 9 and 11.

Another straightforward option is simply \( \sqrt{100} + \sqrt{7} \), since \( \sqrt{7} \) is irrational and approximately equals 2.646, which gives us around \( 10.646 \), still between 9 and 11.