Question

Find the geometric mean between the two numbers.

$22$and $55$

Short answer

Geometric mean is $5\sqrt{55}$.

Step-by-step solution

Step 1. Given information.

The given two numbers are,

$25$ and $55$

Step 2. Formula used.

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

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

Here,

$\begin{array}{c}{a}_1=25\\ a_2=55\end{array}$

Step 3. Calculate the mean.

$\begin{array}{c}\text{Mean}=\sqrt{a_1\times a_2}\\ =\sqrt{25\times 55}\\ =\sqrt{5^2\times 55}\\ =5\sqrt{55}\end{array}$

Step 4. Neglect negative sign.

Since, square root is positive quantity.

Therefore, the geometric mean between the two numbers $25$ and $55$ is $5\sqrt{55}$.