Question 193957
These  problems  can  be  solved by  "distribution"  just  like  an  (x+y)(2x+2y) problem
In  fact,  we  can  use  the  FOIL  technique  here
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( 5 +2 sqrt3 ) * ( 4 - 5 sqrt2 )
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20 - 25 sqrt2 +8 sqrt3 -10 sqrt6,,,,,,,,,,,(sqrt3 *sqrt2 = sqrt6)
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we  should  look  to  combine  like  terms,,,in  this  case  no
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and  to  remove  any  perfect  squares  due  to  multiplying  two  sq rts,,,in  this  case  no
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ANSWER  is ,,,,, 20 - 25 sqrt 2 +8 sqrt 3 -10 sqrt 6
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check  by  using  calculator  on  original,  and  on  answer,  ok  both  give  -26