how do you find the geometric mean of two numbers?

Question

ash2326 · Answer

Suppose we have two numbers a and b
their Geometric Mean is given as
$$ \sqrt{ab}$$

anonymous · Answer

so i multiply them and then find the squareroot?

ash2326 · Answer

yeah

anonymous · Answer

ok

anonymous · Answer

i got a decimal and none of my choices are a decimal :/

hero · Answer

The proper equation is

$$\frac{x}{a} = \frac{b}{x}$$

Then cross multiply to get
$$x^2 = ab$$

Then square root both sides to get
$$x = \sqrt{ab}$$

myininaya · Answer

and of n numbers
it is 
$$GM=\sqrt[n]{x_1x_2x_3 \cdots x_n}$$

anonymous · Answer

ok, the two number i ahev is 5 and 15. and i cross multiplied and got 75, and the squareroot of 75 is 8.66025.... but none of the answers has a decimal. but one of them does have 8. so im alil confused here

hero · Answer

sqrt{25*3) = 5 root{3}

myininaya · Answer

$$GM=\sqrt{5 \cdot 15} =\sqrt{5 \cdot 5 \cdot 3} =5 \sqrt{3}$$
yeah what hero said