Explanation

The mean proportional between two numbers a and b is a number x such that: a : x :: x : b

In this case, we want to find the mean proportional between 64 and 81.

Let's set up the proportion: 64 : x :: x : 81

We can rewrite this as: 64/x = x/81

Cross-multiplying, we get: 64 × 81 = x^2

Simplifying, we get: 5184 = x^2

Taking the square root of both sides, we get:

x = √5184

x = 72

So, the mean proportional between 64 and 81 is 72.