1) 2/(5√3)=(2(5√3))/((5√3)(5√3))=(2(5√3))/75=(2√3)/15
2) (√5+2)/(√5-2)=((√5+2)(√5+2))/((√5-2)(√5+2))=(5+4√5+4)/(5-4)=(9+4√5)/1=9+4√5
3) 17/(3√2+1)=(17(3√2-1))/((3√2+1)(3√2-1))=(17(3√2-1))/(18-1)=(17(3√2-1))/17=3√2-1
4) 4/(2√5+√3)=(4(2√5-√3))/((2√5+√3)(2√5-√3))=(8√5-4√3)/(20-3)=(8√5-√3)/17