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what is -5 squared

what is -5 squared

less than a minute read 05-02-2025
what is -5 squared

The question "What is -5 squared?" often trips people up. It highlights a crucial point about the order of operations in mathematics. Let's break it down to understand the correct answer and avoid common misconceptions.

Understanding the Order of Operations (PEMDAS/BODMAS)

Before tackling -5 squared, remember the order of operations. This dictates the sequence in which we perform calculations:

  • Parentheses/Brackets: Operations within parentheses (or brackets) are done first.
  • Exponents/Orders: Exponents (powers) are calculated next.
  • Multiplication and Division: These operations are performed from left to right.
  • Addition and Subtraction: These are performed from left to right.

Many people remember this order using the acronym PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) or BODMAS (Brackets, Orders, Division, Multiplication, Addition, Subtraction).

Calculating -5 Squared

Now, let's apply this to -5 squared, which is written as (-5)²:

  1. Parentheses: The parentheses around -5 are crucial. They indicate that the entire -5 is being squared, not just the 5.

  2. Exponents: The exponent (²) means we multiply the base (-5) by itself: (-5) * (-5) = 25

Therefore, (-5)² = 25

The Difference Between (-5)² and -5²

This is where the confusion often arises. Note the difference between (-5)² and -5²:

  • (-5)²: This means (-5) multiplied by itself. The negative sign is included within the squaring operation. This results in a positive answer.

  • -5²: This means the negative of 5 squared. Here, the squaring operation only applies to the 5, and the negative sign is applied afterward. This results in a negative answer. The calculation is (5²) * -1 = -25

In short: Parentheses are key! They determine whether the negative sign is included in the squaring.

Common Mistakes to Avoid

A common error is to calculate -5² as (-5)², leading to an incorrect answer. Remember, the exponent only applies to the number directly preceding it unless parentheses are used to explicitly group terms differently.

Conclusion

Understanding the order of operations, particularly when dealing with negative numbers and exponents, is crucial for accurate calculations. (-5)² equals 25 because the parentheses enclose the negative sign, making it part of the base that is squared. Always pay attention to the placement of parentheses and the order of operations to avoid common errors.

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