Solve the Expression: Square Root of 144 Plus 12

Q: How do I know that √144 equals 12?

Ask yourself: what number times itself equals 144? Since 12 × 12 = 144, we know that $ \sqrt{144} = 12 $. This is a perfect square you should memorize!

Q: Why don't I add first, then take the square root?

Because of the order of operations! Square roots are calculated before addition. The expression $ \sqrt{144} + 12 $ means "square root of 144, then add 12."

Q: What's the difference between √144 + 12 and √(144 + 12)?

Huge difference! $ \sqrt{144} + 12 = 12 + 12 = 24 $, but $ \sqrt{144 + 12} = \sqrt{156} ≈ 12.49 $. Parentheses change everything in the order of operations!

Q: Are there other perfect squares I should know?

Yes! Memorize these common ones: 1² = 1, 2² = 4, 3² = 9, 4² = 16, 5² = 25, 6² = 36, 7² = 49, 8² = 64, 9² = 81, 10² = 100, 11² = 121, 12² = 144, 13² = 169, 14² = 196, 15² = 225.

Square Root Operations with Perfect Squares

$\sqrt{144}+12=$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:05 Square root of any number (X) squared, root cancels square

00:08 Let's use this formula in our exercise

00:11 Let's break down 144 to 12 squared

00:17 Root and square cancel out

00:20 Let's calculate and solve

00:24 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\sqrt{144}+12=$

Step-by-step solution

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

Step 1: Calculate the square root of 144.
Step 2: Add 12 to the result of the square root.

Now, let's work through each step:
Step 1: The square root of 144 is $\sqrt{144} = 12$ , since 12 is the number that, when squared, gives 144.
Step 2: Add 12 to this result, which is $12 + 12 = 24$ .

Therefore, the solution to the problem is $24$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Perfect Squares: Recognize that 144 = 12² for quick calculation
Technique: Calculate $\sqrt{144} = 12$ , then add: 12 + 12 = 24
Check: Verify that 12 × 12 = 144, so our calculation is correct ✓

Common Mistakes

Avoid these frequent errors

Adding 12 before taking the square root
Don't calculate √(144 + 12) = √156 ≈ 12.49! This changes the order of operations and gives a completely wrong answer. Always calculate the square root first: √144 = 12, then add 12.

Practice Quiz

Test your knowledge with interactive questions

$\sqrt{100}=$

FAQ

Everything you need to know about this question

How do I know that √144 equals 12?

Ask yourself: what number times itself equals 144? Since 12 × 12 = 144, we know that $\sqrt{144} = 12$ . This is a perfect square you should memorize!

What if I don't remember that 144 is a perfect square?

You can work backwards! Try numbers: 10² = 100 (too small), 15² = 225 (too big), so try numbers between them. Or use factoring: 144 = 12 × 12.

Why don't I add first, then take the square root?

Because of the order of operations! Square roots are calculated before addition. The expression $\sqrt{144} + 12$ means "square root of 144, then add 12."

What's the difference between √144 + 12 and √(144 + 12)?

Huge difference! $\sqrt{144} + 12 = 12 + 12 = 24$ , but $\sqrt{144 + 12} = \sqrt{156} ≈ 12.49$ . Parentheses change everything in the order of operations!

Are there other perfect squares I should know?

Yes! Memorize these common ones: 1² = 1, 2² = 4, 3² = 9, 4² = 16, 5² = 25, 6² = 36, 7² = 49, 8² = 64, 9² = 81, 10² = 100, 11² = 121, 12² = 144, 13² = 169, 14² = 196, 15² = 225.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Powers and Roots - Basic questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime