Question

Find the additive inverse of each of the following: $(-3+\sqrt{3}{)}^2$

Answer 1

We know that the additive inverse of a number $x$ is $-x$, which when added to $x$ yields the additive identity $0$ that is

$x+(-x)=x-x=0$

Now, since

${(-3+\sqrt{3})}^2+[-{(-3+\sqrt{3})}^2]={(-3+\sqrt{3})}^2-{(-3+\sqrt{3})}^2=0$

Hence, the additive inverse of ${(-3+\sqrt{3})}^2$ is ${-(-3+\sqrt{3})}^2$.