# What is the distance between (0, 0, 8)  and (3, 4, 1) ?

Dec 23, 2015

$\sqrt{74} \approx 8.6$

#### Explanation:

By the distance formula, the distance between two points $P$ and $Q$ whose rectangular coordinates are $\left({x}_{1} , {y}_{1} {,}_{z} _ \left\{1\right\}\right)$ and $\left({x}_{2} , {y}_{2} , {z}_{2}\right)$ is

$\sqrt{{\left({x}_{1} - {x}_{2}\right)}^{2} + {\left({y}_{1} - {y}_{2}\right)}^{2} + {\left({z}_{1} - {z}_{2}\right)}^{2}}$

For the problem at hand, this is

$\sqrt{{\left(3 - 0\right)}^{2} + {\left(4 - 0\right)}^{2} + {\left(1 - 8\right)}^{2}} = \sqrt{9 + 16 + 49} = \sqrt{74} \approx 8.6$.