Question

Find the geometric mean between the two numbers.

$1$ and $1000$

Short answer

Geometric mean is $10\sqrt{10}$.

Step-by-step solution

Step 1. Given information.

The given two numbers are,

$1$and $1000$

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

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

Here,

$\begin{array}{c}{a}_1=1\\ a_2=1000\end{array}$

Step 3. Calculate the mean.

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

$\begin{array}{c}\sqrt{1\cdot 1000}=\sqrt{1000}\\ =\sqrt{100\cdot 10}\\ =\sqrt{100}\cdot \sqrt{10}\\ =10\sqrt{10}\end{array}$

Step 4. Neglect negative sign.

Since, square root is positive quantity.

Therefore, the geometric mean between the two numbers $1$ and $1000$ is $10\sqrt{10}$.