Case Study

Quality Control: Bracket Surface Area

A quality control technician is verifying the surface area of two square metal brackets. The side length of Bracket A is recorded in the system as 19\sqrt{19} inches, and the side length of Bracket B is recorded as −19-\sqrt{19} inches. To calculate the area of each bracket, the technician must square these side lengths: (19)2(\sqrt{19})^2 and (−19)2(-\sqrt{19})^2.

Identify the simplified numerical result for both expressions and state the mathematical rule that explains why the result of (−19)2(-\sqrt{19})^2 is positive.

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Updated 2026-09-17

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