Evaluate |5² - 24|: Absolute Value of Perfect Square Minus 24

Q: Why do I calculate the exponent before subtracting?

You follow the order of operations (PEMDAS)! Exponents come before subtraction, so $ 5^2 $ must be calculated first to get 25, then subtract 24.

Q: What if the result inside the absolute value bars was negative?

Great question! If $ 5^2 - 24 $ gave us -1 instead, then $ |-1| = 1 $. Absolute value always gives a positive result or zero.

Q: Do I need to show all my steps?

Yes, definitely! Show: 1) Calculate the exponent, 2) Do the subtraction, 3) Find absolute value. This prevents errors and shows your understanding.

Q: Can absolute value bars work like parentheses?

Exactly! Treat absolute value bars $ | | $ like parentheses - complete everything inside first using order of operations, then find the absolute value of that result.

Q: What's the difference between |25| and |-25|?

Both equal 25! Absolute value gives the distance from zero, so $ |25| = 25 $ and $ |-25| = 25 $. The result is always positive or zero.

Absolute Value with Perfect Square Calculations

$|5^2 - 24| =$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$|5^2 - 24| =$

Step-by-step solution

First, calculate $5^2$ . That is, $5 \times 5 = 25$ .

Next, subtract 24 from 25: $25 - 24 = 1$ .

Finally, the absolute value of 1 is $|1| = 1$ since it is already a positive number.

Final Answer

$1$

Key Points to Remember

Essential concepts to master this topic

Order: Calculate exponent first, then subtract, finally find absolute value
Technique: $5^2 = 25$ , then $25 - 24 = 1$
Check: Since 1 is positive, $|1| = 1$ confirms our answer ✓

Common Mistakes

Avoid these frequent errors

Finding absolute value before completing all operations
Don't find |5²| - 24 = 25 - 24 = 1! This ignores order of operations and can give wrong answers when the expression inside absolute value bars is negative. Always complete all operations inside the absolute value bars first, then find the absolute value.

Practice Quiz

Test your knowledge with interactive questions

Determine the absolute value of the following number:

$\left|18\right|=$

FAQ

Everything you need to know about this question

Why do I calculate the exponent before subtracting?

You follow the order of operations (PEMDAS)! Exponents come before subtraction, so $5^2$ must be calculated first to get 25, then subtract 24.

What if the result inside the absolute value bars was negative?

Great question! If $5^2 - 24$ gave us -1 instead, then $|-1| = 1$ . Absolute value always gives a positive result or zero.

Do I need to show all my steps?

Yes, definitely! Show: 1) Calculate the exponent, 2) Do the subtraction, 3) Find absolute value. This prevents errors and shows your understanding.

Can absolute value bars work like parentheses?

Exactly! Treat absolute value bars $| |$ like parentheses - complete everything inside first using order of operations, then find the absolute value of that result.

What's the difference between |25| and |-25|?

Both equal 25! Absolute value gives the distance from zero, so $|25| = 25$ and $|-25| = 25$ . The result is always positive or zero.

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