1. The problem asks to identify the false statement among the given options about absolute values and square roots. 2. Let's analyze each statement: (a) $|xy| = |x||y|$ is true because the absolute value of a product equals the product of the absolute values. (b) $|x| = |-x|$ is true since absolute value measures distance from zero, so $x$ and $-x$ have the same absolute value. (c) $|x + y| = |x| + |y|$ is generally false. The absolute value of a sum is less than or equal to the sum of absolute values (triangle inequality), but not always equal. (d) $\sqrt{x^2} = |x|$ is true because the square root of $x^2$ is the non-negative value of $x$, which is the absolute value. 3. Therefore, the false statement is (c). Final answer: (c) $|x + y| = |x| + |y|$ is false.