The geometric mean x of two numbers is the positive value of x that satisfies the proportion a/x =x/b, where a and b are given. Find the geometric mean of 16 and 9.

16/x = x/9 , cross-multiply

x^2= 144
x = √144 = 12

check:
16/12 = 4/3
12/9 = 4/3

Thanks. So the geometric mean for 16 and 9 is 4/3?

NOOO, the geometric mean is 12

I merely showed that 12 is correct
and satisfied your given proportion
a/x = x/b

the 3 numbers are:
16 , 12 , 9 , with 12 as the geometric mean

Oh okay...thanks.

To find the geometric mean of two numbers, you can use the formula x = sqrt(a * b), where a and b are the given numbers.

In this case, a = 16 and b = 9.

1. Start by substituting the given values in the formula:
x = sqrt(16 * 9)

2. Multiply the two numbers inside the square root:
x = sqrt(144)

3. Simplify the square root:
x = 12

Therefore, the geometric mean of 16 and 9 is 12.