The problem asks us to find the geometric mean of 81 and 121.

1. Problem Description

The problem asks us to find the geometric mean of 81 and

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2. Solution Steps

The geometric mean of two numbers $a$ and $b$ is given by $\sqrt{ab}$.

In this case, we have $a = 81$ and $b = 121$.

So the geometric mean is $\sqrt{81 \times 121}$.

We know that $81 = 9^2$ and $121 = 11^2$.

Therefore, the geometric mean is $\sqrt{9^2 \times 11^2}$.

This can be simplified to $\sqrt{(9 \times 11)^2}$.

Taking the square root gives us $9 \times 11$.

$9 \times 11 = 99$.

3. Final Answer

The geometric mean of 81 and 121 is 99.