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Figure 1

2  - root(3)
       Draw AB of  1 unit, and BC of 2 units at 60° deg to AB.   Draw AD = 2 units.  so answer CD is  2 - root(3).

figure 2

     draw BC of 3 units,  AB and AC at 45 deg.  intersection is A. Now draw arc AD = AB on extended CA.  Now araw an arc  2 units from C , to cut at E.  DE is  2 - root(3)

figure 3

3 - root(2)
Draw BD 3 units.  At B draw BA at 45 deg. of length 1 unit.  Now at A draw a perpendicular to AB of length 1 meets BD at C.  Now BC is root (2)..    CD = 3 - root (2)    

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