TITLE: Divide a line segment in the ratio $\sqrt{2}:\sqrt{3}.$
QUESTION [9 upvotes]: "Divide a line segment in the ratio $\sqrt{2}:\sqrt{3}.$"
I have got this problem in a book, but I have no idea how to solve it.
Any help will be appreciated.

REPLY [3 votes]: Draw an isosceles rectangle triangle. Carry the hypothenuse on a side. If the hypothenuse is $\sqrt2$, the new segment is $\sqrt3$.

By Thales' theorem you can divide any segment in this ratio.