The question: please find the distance between the two points,

\((1,\sqrt{2}) (5,\sqrt{8})\)

I don't know what my mistake was but here is how i approached this problem...

\( d=\sqrt{(-4)^2+(-2)^2} d= \sqrt{16+4} d=\sqrt{20} =2\sqrt{5} \)

Can someone please tell me how to solve this?

Nirvana Jun 10, 2019

#1**+5 **

\(d\ =\ \sqrt{(1-5)^2+(\sqrt2-\sqrt8)^2} \) But \(\sqrt2-\sqrt8\ \neq\ -2\) !!

\(d\ =\ \sqrt{(1-5)^2+(\sqrt2-2\sqrt2)^2}\) because \(\sqrt8\ =\ 2\sqrt{2}\)

\(d\ =\ \sqrt{(1-5)^2+(-\sqrt2\,)^2}\) because x - 2x = -x so \(\sqrt2-2\sqrt2\ =\ -\sqrt2\)

\(d\ =\ \sqrt{(-4)^2+(-\sqrt2\,)^2}\) because 1 - 5 = -4

\(d\ =\ \sqrt{16+2}\) because \((-4)^2=16\) and \((-\sqrt2)^2=2\)

\(d\ =\ \sqrt{18}\)

\(d\ =\ 3 \sqrt{2}\)_

hectictar Jun 10, 2019