How do you simplify $(5+sqrt3)(5-sqrt3)$ ?

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Answer 1 · 2015-06-05T21:41:06

This is of the form $(a+b)(a-b)$ with $a=5$ and $b=sqrt(3)$

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

So

$(5+sqrt(3))(5-sqrt(3)) = 5^2-(sqrt(3))^2 = 25 - 3 = 22$

How do you simplify (5+sqrt3)(5-sqrt3)(5+sqrt3)(5-sqrt3)?