# Geometric mean of $$$5$$$, $$$12$$$

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### Your Input

**Find the geometric mean of $$$5$$$, $$$12$$$.**

### Solution

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 $$$\left(5\right)\cdot \left(12\right) = 60$$$.

Therefore, the geometric mean is $$$\sqrt{60} = 2 \sqrt{15}$$$.

### Answer

**The geometric mean is $$$2 \sqrt{15}\approx 7.745966692414834$$$A.**