Compass-and-straightedge construction of the square root of a given line?

manpreet Best Answer 3 years ago

Given

1. A straight line of arbitrary length
2. The ability to construct a straight line in any direction from any starting point with the "unit length", or the length whose square root of its magnitude yields its own magnitude.

Is there a way to geometrically construct (using only a compass and straightedge) the a line with the length of the square root of the arbitrary-lengthed line? What is the mathematical basis?

Also, why can't this be done without the unit line length?