Geometric Mean

• Jan 5th 2009, 03:37 PM
algebraisabeast
Geometric Mean
Find the geometric mean between
$$\frac{2\sqrt{2}}{6}$$* $$\frac{5\sqrt{2}}{6}$$

so we multiply the numbers together then take the sqrt of that number.

I get $$\frac{9\sqrt{5}}{18}$$
I am told the answer is $$\frac{\sqrt{5}}{3}$$

Thanks if anyone looked found error, feel dumb know Thank you
• Jan 5th 2009, 03:42 PM
HallsofIvy
Quote:

Originally Posted by algebraisabeast
Find the geometric mean between
$$\frac{2\sqrt{2}}{6}$$ $$\frac{5\sqrt{2}}{6}$$

The "geometric mean" of two numbers, a and b, is $\sqrt{ab}$
so the geometric mean between $\frac{2\sqrt{2}}{6}$ and $\frac{5\sqrt{2}}{6}$ is $\sqrt{\frac{2\sqrt{2}}{6}\frac{5\sqrt{2}}{6}}= \frac{\sqrt{20}}{6}= \frac{2\sqrt{5}}{6}$