Show an example of an irrational number between nine and eleven

Answer 1

An example of an irrational number between nine and eleven is \( \sqrt{90} \).

To confirm that it is indeed between 9 and 11, we can evaluate it:

\[ 9^2 = 81 \quad \text{and} \quad 11^2 = 121 \]

Since \( 90 \) is between \( 81 \) and \( 121 \), it follows that:

\[ 9 < \sqrt{90} < 11 \]

Thus, \( \sqrt{90} \) is an irrational number that lies between nine and eleven.