Question

一道根式数学题√(6+√8+√12+√24)=?

Answer 1

√(6+√8+√12+√24)

=√(6+2√2+2√3+2√6)

=√(6+2√6+2√2+2√3)

=√(2+3+1+2√2√3+2√2+2√3)

=√[(2+2√2√3+3)+(2√2+2√3+1)]

=√[(√2+√3)^2+2(√2+√3)+1]

=√(√2+√3+1)^2

=√2+√3+1