PLEASE HELP! NEED HELP WITH GEOMETRY HOMEWORK!

Question

Identify the geometric mean of 10 and 18 in simplest radical form. Please Give the Explanation and the Answer. Thank You Very Much!

Answer 1

geometric mean is the square root of the product, 18x10

=square root of 180

180=9x4x5 = 36x5

square root of 36 is 6, square root of 36x5

=6(5)^1/2

check the answer and square it to get 36x5 = 180

Answer 2

Definition: Geometric mean of A and B is A/x = x/B

which by cross multiplication is x^2 = AB

10/x = x/18

x^2 = 18*10

x^2 = 180

x = square root of 180

= square root of (18 * 10)

= square root of [( 3*3 * 2) *( 2 * 5)]

pairs factor out

2*3 * square root (5)

6 * square root(5)