SOLUTION: multiply ( 2sqrt(3) - 4sqrt(6) )( 3sqrt(3) + 6sqrt(6) )

Algebra ->  Radicals -> SOLUTION: multiply ( 2sqrt(3) - 4sqrt(6) )( 3sqrt(3) + 6sqrt(6) )      Log On


   



Question 358123: multiply

( 2sqrt(3) - 4sqrt(6) )( 3sqrt(3) + 6sqrt(6) )

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%28+2sqrt%283%29+-+4sqrt%286%29+%29%28+3sqrt%283%29+%2B+6sqrt%286%29+%29
This expression is similar to
(2x - 3y)(3x + 6y)
and we do the same thing to multiply: Use FOIL (or whatever technique you have learned to multiply polynomials):

Within each product we will multiply the coefficients and use the property of radicals, root%28a%2C+p%29%2Aroot%28a%2C+q%29+=+root%28a%2C+p%2Aq%29, to multiply the square roots:
6sqrt%283%2A3%29+%2B+12sqrt%283%2A6%29+-12sqrt%286%2A3%29+-24sqrt%286%2A6%29
which simplifies as follows:
6sqrt%289%29+%2B+12sqrt%2818%29+-12sqrt%2818%29+-24sqrt%2836%29
Since sqrt%289%29+=+3 and sqrt%2836%29+=+6 and since the two middle terms cancel out:
6%2A3+-24%2A6
18+-+144
-126
So
%28+2sqrt%283%29+-+4sqrt%286%29+%29%28+3sqrt%283%29+%2B+6sqrt%286%29+%29+=+-126