Simplifying √29−4√5+√39+4√5.
√29−4√5+√39+4√5=√2(9+4√5)+√3(9−4√5)(9−4√5)(9+4√5)
=9√2+4√10+9√3−4√15(9)2−(4√5)2
=9(√2+√3)+4(√10−√15)81−80
=9(√2+√3)+4(√10−√15)