Question

化简 根号下 11/2-根号30 和 根号下 3+ 2根号下 5+12根号下 3+2根号2

Answer 1

√[11/2-√30]

=√[(11-2√30)/2]

=√[(√6-√5)^2/2]

=(√6-√5)√(1/2)

=(√6-√5)√2/2

=(√12-√10)/2

√{3+2√[5+12√(3+2√2)]}

=√{3+2√[5+12√(1+√2)^2]}

=√{3+2√[5+12(1+√2)]}

=√{3+2√[5+12+12√2]}

=√{3+2√[17+12√2)]}

=√{3+2√[2√2+3]^2}

=√{3+2(2√2+3)}

=√{3+4√2+6}

=√{9+4√2}

=√{2√2+1}^2

=2√2+1