What's the geometric mean of 5 and 10?

The geometric mean of 5 and 10 is the positive square root of the product.

SQR (5*10) = SQR (50) = SQR (25 * 2) = 5 SQR (2)

If you are in Geometry and using proportions,

5/x = x/10 where x is the geomtric mean.

x^2 is 50 and x = 5 SQR (2)