[Math] The set of all real numbers $x$ such that $\sqrt{x^2}=-x$

absolute valuealgebra-precalculusradicals

The questions goes as

The set of all real numbers $x$ such that $\sqrt{x^2} = -x$ consists of

a. Zero only
b. Nonpositive real numbers only
c. positive real numbers only
d. all real numbers
e. no real numbers

I chose b but I don't completely understand. I learned that the term "nonpositive real numbers" means that $0$ is included with all the numbers to negative infinity. I know that all positive real numbers have two square roots. Can someone explain this to me please?

Best Answer

You have $\sqrt{x^2} = |x|$. Now the answer becomes clear.