# How do you find the distance between (sqrt6,-6sqrt5), (2sqrt6,sqrt5)?

Jan 18, 2017

When given two points, $\left({x}_{0} , {y}_{0}\right) \mathmr{and} \left({x}_{1} , {y}_{1}\right)$, the distance, d, between them is:

$d = \sqrt{{\left({x}_{1} - {x}_{0}\right)}^{2} + {\left({y}_{1} - {y}_{0}\right)}^{2}}$

#### Explanation:

Given: $\left(\sqrt{6} , - 6 \sqrt{5}\right) \mathmr{and} \left(2 \sqrt{6} , \sqrt{5}\right)$

The distance is:

$d = \sqrt{{\left(2 \sqrt{6} - \sqrt{6}\right)}^{2} + {\left(\sqrt{5} - - 6 \sqrt{5}\right)}^{2}}$

$d = \sqrt{{\left(\sqrt{6}\right)}^{2} + {\left(7 \sqrt{5}\right)}^{2}}$

$d = \sqrt{6 + 245}$

$d = \sqrt{251}$

$d \approx 15.84$