Question

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

Answer 1

`(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.