1.
2.
3.
4.
1. Setting up the problem to find the geometric mean between 4 and 16:
First let x be the geometric mean. We know that x divided by 4 equals 16 divided by x or
2. Solving for the geometric mean:
First we start with our equation from 1, then cross multiply:
The geometric mean between two positive numbers is positive, so we only want the positive solution.
We have two positive numbers a and b such that a < b. We know the geometric mean will be a positive number, x, such that the ratios and will be the same or
cross multiplying gives us:
taking the square roots of both sides (keeping only the positive solution) gives us:
.