Solve |3²|: Evaluating Absolute Value of a Square Number

Q: Why is the absolute value of 9 still 9?

Absolute value measures distance from zero on the number line. Since 9 is already positive, it's already 9 units away from zero, so $ |9| = 9 $.

Q: What if the number inside was negative?

If you had $ |(-3)^2| $, you'd still get 9! First: $ (-3)^2 = (-3) \times (-3) = 9 $, then $ |9| = 9 $. Any number squared becomes positive!

Q: Do I need absolute value bars if the answer is already positive?

Yes, you should still show your work! Even though $ 3^2 = 9 $ is positive, the problem asks for $ |3^2| $, so write $ |9| = 9 $ to show you understand absolute value.

Q: What's the difference between |3²| and |3|²?

Great question! $ |3^2| $ means "square 3 first, then take absolute value" = $ |9| = 9 $. While $ |3|^2 $ means "take absolute value first, then square" = $ 3^2 = 9 $. Always follow order of operations!

Q: Can absolute value ever make a number smaller?

No! Absolute value either keeps a positive number the same or makes a negative number positive. It represents distance, which is always positive or zero.

Absolute Value with Perfect Squares

$\left|3^2\right|=$

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Understand the problem

$\left|3^2\right|=$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Calculate the square of 3.
Step 2: Determine the absolute value of the result.

Now, let's work through each step:
Step 1: Calculate $3^2$ .
The square of 3 is calculated as follows: $3 \times 3 = 9$ .

Step 2: Apply the concept of absolute value.
Since $9$ is already positive, the absolute value of $9$ is simply $9$ , as $|9| = 9$ .

Therefore, the solution to the problem is $9$ , which corresponds to choice 3 in the provided options.

Final Answer

$9$

Key Points to Remember

Essential concepts to master this topic

Order: Always calculate the exponent first, then apply absolute value
Technique: Square first: $3^2 = 3 \times 3 = 9$
Check: Positive numbers stay positive: $|9| = 9$ ✓

Common Mistakes

Avoid these frequent errors

Applying absolute value before calculating the exponent
Don't solve $|3|^2 = 3^2 = 9$ instead of $|3^2|$ ! While this gives the same answer here, it creates confusion about order of operations. Always calculate exponents first, then apply absolute value: $|3^2| = |9| = 9$ .

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 is the absolute value of 9 still 9?

Absolute value measures distance from zero on the number line. Since 9 is already positive, it's already 9 units away from zero, so $|9| = 9$ .

What if the number inside was negative?

If you had $|(-3)^2|$ , you'd still get 9! First: $(-3)^2 = (-3) \times (-3) = 9$ , then $|9| = 9$ . Any number squared becomes positive!

Do I need absolute value bars if the answer is already positive?

Yes, you should still show your work! Even though $3^2 = 9$ is positive, the problem asks for $|3^2|$ , so write $|9| = 9$ to show you understand absolute value.

What's the difference between |3²| and |3|²?

Great question! $|3^2|$ means "square 3 first, then take absolute value" = $|9| = 9$ . While $|3|^2$ means "take absolute value first, then square" = $3^2 = 9$ . Always follow order of operations!

Can absolute value ever make a number smaller?

No! Absolute value either keeps a positive number the same or makes a negative number positive. It represents distance, which is always positive or zero.

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