Geometric mean of $$$20$$$, $$$27$$$

Find the geometric mean of $$$20$$$, $$$27$$$.

The geometric mean of data is given by the formula $$$\left(\prod_{i=1}^{n} x_{i}\right)^{\frac{1}{n}}$$$, where $$$n$$$ is the number of values and $$$x_i, i=\overline{1..n}$$$ are the values themselves.

Since we have $$$2$$$ points, $$$n = 2$$$.

The product of the values is $$$\left(20\right)\cdot \left(27\right) = 540$$$.

Therefore, the geometric mean is $$$\sqrt{540} = 6 \sqrt{15}$$$.

The geometric mean is $$$6 \sqrt{15}\approx 23.237900077244501$$$A.