# How do you find the domain of square root of 1-x^2?

$\sqrt{1 - {x}^{2}}$ has the domain $\left[- 1 , 1\right]$.
A square root with a negative number under the root cannot produce a real number. This means that $1 - {x}^{2}$ must be greater than or equal to zero.
Squaring a real number will always produce a positive number, so ${x}^{2}$ must be equal to or smaller than $1$. This means $x$ is between $0$ and $1$, giving the domain of $\left[0 , 1\right]$.