How do you simplify (6+ square root 3)(6-square root 3)?

1 Answer
Jul 20, 2015

Answer:

#(6+sqrt(3))*(6-sqrt(3))=6^2-(sqrt(3))^2=36-3=33#

Explanation:

General property this problem is based upon is
#(a+b)*(a-b)=a^2-b^2#

Indeed, if we open the parenthesis in the original expression, we get:
#(a+b)*(a-b)=a*a+b*a-a*b-b*b=a^2-b^2#

Using the above property for #a=6# and #b=sqrt(3)#, we obtain
#(6+sqrt(3))*(6-sqrt(3))=6^2-(sqrt(3))^2=36-3=33#

So, #33# is the final answer.