Exercises: Terms with Square Roots

For which values of $x$ are the following statements true?

$\sqrt{x^{2}} = - x$

For this task you need the following basic knowledge: Square Roots
For which $x$ do we have $\sqrt{x^{2}} = - x$ ?
In general, we have $\sqrt{x^{2}} = | x |$ . So:
For which $x$ is it true that $| x | = - x$ ?
Answer: For all values of $x$ that are less than or equal to $0$ .
$\sqrt{{(x - 1)}^{2}} = x - 1$

For this task you need the following basic knowledge: Square Roots
This is true for all values $x \geq 1$ , since $\sqrt{{(x - 1)}^{2}} = | x - 1 |$ and the absolute value function is equal to the right-hand side exactly for $x - 1 \geq 0$ .

This content is licensed under
CC BY-SA 4.0 → What does that mean? serlo.org