How do you simplify (6+ sqrt3)(6-sqrt3)?

1 Answer
George C.
May 28, 2015

You may find it helpful to use the mnemonic FOIL - First, Outside, Inside, Last.

That means multiply both first terms together (6xx6),
add the product of the outside terms (6xx-sqrt(3))
add the product of the inside terms (sqrt(3)xx6)
add the product of the last terms (sqrt(3)xx-sqrt(3))

So

(6+sqrt(3))(6-sqrt(3))

= 6^2-cancel(6sqrt(3))+cancel(6sqrt(3))-sqrt(3)^2

= 36-3 = 33

Alternatively, you could use the identity of difference of squares:

a^2-b^2 = (a-b)(a+b)

to get:

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

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