√[16+2(1+√5)(1+2√3)]
=√(18+4√3+2√5+4√15)
=√[1+4√3+2√5+12+4√15+5]
=√[1+4√3+2√5+(2√3)²+2(2√3)(√5)+(√5)²]
=√[1+2(2√3+√5)+(2√3+√5)²]
=√[(1+2√3+√5)²]
=1+2√3+√5