Question

化简根号[16+2(1+根号5)(1+2又根号3)]

Answer 1

√[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