Question

Find the geometric mean between the two numbers.

$16$and $24$

Short answer

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

Step-by-step solution

Step 1. Given information.

The given two numbers are,

$16$ and $24$

Step 2. Formula used.

Geometric mean between two numbers $a$and $b$

$r=\sqrt{a_1\times a_2}$

Here,

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

Step 3. Calculate the mean.

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

Step 4. Neglect negative sign.

Since, square root is positive quantity.

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