SOLUTION: I'm trying to prove that {{{sqrt(4 - 2 * sqrt(3)) + sqrt(12 - 6 * sqrt(3)) = 2}}}

Algebra ->  Radicals -> SOLUTION: I'm trying to prove that {{{sqrt(4 - 2 * sqrt(3)) + sqrt(12 - 6 * sqrt(3)) = 2}}}      Log On


   

Question 681800: I'm trying to prove that
sqrt%284+-+2+%2A+sqrt%283%29%29+%2B+sqrt%2812+-+6+%2A+sqrt%283%29%29+=+2
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%284+-+2+%2A+sqrt%283%29%29+%2B+sqrt%2812+-+6+%2A+sqrt%283%29%29+=+2
2sqrt%281+-+0.5sqrt%283%29%29+%2B+sqrt%2812%29%2Asqrt%281+-+0.5sqrt%283%29%29+=+2
%282+%2B+2sqrt%283%29%29%2Asqrt%281+-+0.5sqrt%283%29%29+=+2
%281+%2B+sqrt%283%29%29%2Asqrt%281+-+0.5sqrt%283%29%29+=+1
Multiply by sqrt(1 + 0.5sqrt(3))
%281+%2B+sqrt%283%29%29%2Asqrt%281+-+0.25%2A3%29+=+sqrt%281+%2B+0.5sqrt%283%29%29
square both sides
%281+%2B+3+%2B+2sqrt%283%29%29%2A%280.25%29+=+1+%2B+0.5sqrt%283%29
1+%2B+0.5sqrt%283%29+=+1+%2B+0.5sqrt%283%29
QED