Question 217286
{{{(6+sqrt(-3))(2-sqrt(-6))}}}


Perform the operation and write the result in standard form.


Step 1.  You can use FOIL to multiply the terms:


{{{(6+sqrt(-3))(2-sqrt(-6))=6*2-6*sqrt(-6)+2*sqrt(-3)-sqrt(-3)*sqrt(-6)}}}



{{{(6+sqrt(-3))(2-sqrt(-6))=12-6sqrt(-6)+2sqrt(-3)-sqrt(-3)*sqrt(-6)}}}


Step 2.  Replace {{{sqrt(-3)=sqrt(-1)*sqrt(3)=i*sqrt(3)}}} and {{{sqrt(-6)=sqrt(-1)*sqrt(6)=i*sqrt(6)}}} where {{{i=sqrt(-1)}}}


Also, {{{sqrt(-3)*sqrt(-6)=i*sqrt(3)*i*sqrt(6)=-1*sqrt(18)=-3*sqrt(2)}}} and {{{i^2=-1}}}


Step 3.  Substitute results in Step 2 into Step 1.


{{{12-6sqrt(-6)+2sqrt(-3)-sqrt(-3)*sqrt(-6)=12-6*i*sqrt(6)+2*i*sqrt(3)-(-3)sqrt(2)}}}


{{{12-6sqrt(-6)+2sqrt(-3)-sqrt(-3)*sqrt(-6)=(12+3sqrt(2))+i*(2sqrt(3)-6sqrt(6))}}}



Step 4.  ANSWER:  {{{(6+sqrt(-3))(2-sqrt(-6))=(12+3sqrt(2))+i*(2sqrt(3)-6sqrt(6))}}}




I hope the above steps and explanation were helpful. 


For Step-By-Step videos on Introduction to Algebra, 

please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and 

for Trigonmetry please visit 

http://www.FreedomUniversity.TV/courses/Trigonometry. 


Also, good luck in your studies and contact me at 

john@e-liteworks.com for your future math needs.


Respectfully, 
Dr J