Evaluate.

[tex]$(-12)^2=$[/tex]

The evaluation of ( − 12 ) 2 involves multiplying -12 by itself, which results in a positive value. Therefore, ( − 12 ) 2 = 144 . This shows that squaring a negative number results in a positive number.
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Answered by Anonymous | 2025-07-04

The problem asks to evaluate ( − 12 ) 2 .
Squaring a number means multiplying it by itself: ( − 12 ) × ( − 12 ) .
A negative number multiplied by a negative number results in a positive number.
Calculate the result: ( − 12 ) 2 = 144 , so the final answer is 144 ​ .

Explanation

Understanding the problem We need to evaluate ( − 12 ) 2 . This means we need to multiply -12 by itself: ( − 12 ) × ( − 12 ) .

Sign of the result When we multiply two negative numbers, the result is a positive number. So, ( − 12 ) × ( − 12 ) will be a positive number.

Calculating the value Now we just need to calculate 12 × 12 . The result is 144.

Final Answer Therefore, ( − 12 ) 2 = 144 .


Examples
Understanding how to square negative numbers is crucial in many areas, such as physics when calculating energy (which is always positive) or in engineering when dealing with alternating currents. For example, when calculating the power dissipated in a resistor, we often square the current, which can be negative depending on the direction of flow. Squaring ensures the power is always a positive value, representing the energy released as heat. This concept is also used in statistics when calculating variance and standard deviation, where deviations from the mean are squared to ensure positive values, preventing negative and positive deviations from canceling each other out.

Answered by GinnyAnswer | 2025-07-04