Chapter 8.1, Problem 20WE

To determine

The geometric mean between the two numbers.

Answer to Problem 20WE

Geometric mean is $8\sqrt{6}$ .

Explanation of Solution

Given information:

The given two numbers are 16 and 24.

Geometric mean (two numbers) = $\sqrt{a_1\times a_2}$

Here,

  $\begin{array}{l}{a}_1=16\\ a_2=24\end{array}$

  $\begin{array}{c}\text{Mean}=\sqrt{a_1\times a_2}\\ =\sqrt{16\times 24}\\ =\sqrt{4^2\times 2^2\times 6}\\ =4\times 2\sqrt{6}\\ =8\sqrt{6}\end{array}$

Since square is positive quantity so neglecting the negative sign.

Therefore, the geometric mean between the two numbers 16 and 24 is $8\sqrt{6}$