there are five points of side two length 2. prove that there exists two of them having a distance not more than square root of 2.

thank you.

Originally Posted by rcs
there are five points of side two length 2. prove that there exists two of them having a distance not more than square root of 2.

thank you.
Do you mean "there are five points inside a square of side two length 2"?
Your statement as is makes no sense at all.

Originally Posted by rcs
there are five points of side two length 2. prove that there exists two of them having a distance not more than square root of 2.

thank you.
Seems like a pidgeon hole. You can hide 4.

Lets assume that this concerns a square that is $2\times 2$.
Suppose we have four smaller squares that are each $1\times 1$. The length of the diagonal of any one the the smaller squares is $\sqrt2$.