Simplify root three plus two
multiplied by root three minus two.
We notice that this expression is
written in the form 𝑥 plus 𝑦 multiplied by 𝑥 minus 𝑦. Using our difference of two squares
result, this is equal to 𝑥 squared minus 𝑦 squared. Our value for 𝑥 is root three, and
our value for 𝑦 is two. 𝑥 squared would therefore be equal
to root three squared. We know that square routing and
squaring are inverse operations. Therefore, 𝑥 squared is equal to
three. 𝑦 squared is equal to four as two
multiplied by two is four. The expression root three plus two
multiplied by root three minus two is equal to three minus four. This is equal to negative one.