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

1 Answer
Zor Shekhtman
Jul 20, 2015

(6+sqrt(3))*(6-sqrt(3))=6^2-(sqrt(3))^2=36-3=33(6+√3)⋅(6−√3)=62−(√3)2=36−3=33

Explanation:

General property this problem is based upon is
(a+b)*(a-b)=a^2-b^2(a+b)⋅(a−b)=a2−b2

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(a+b)⋅(a−b)=a⋅a+b⋅a−a⋅b−b⋅b=a2−b2

Using the above property for a=6a=6 and b=sqrt(3)b=√3, we obtain
(6+sqrt(3))*(6-sqrt(3))=6^2-(sqrt(3))^2=36-3=33(6+√3)⋅(6−√3)=62−(√3)2=36−3=33

So, 3333 is the final answer.

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