Asked by DL
Show an example of an irrational number between nine and eleven
Answers
Answered by
GPT-4o mini
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.
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.
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