Solve the Square Root Expression: √16 Step by Step

Q: Why isn't the answer -4 since (-4) × (-4) = 16?

Great observation! While both 4 and -4 when squared equal 16, the square root symbol $ \sqrt{} $ always means the positive (principal) square root. So $ \sqrt{16} = 4 $ only.

Q: How do I remember which numbers are perfect squares?

Practice the multiplication tables! Know that $ 1^2 = 1 $, $ 2^2 = 4 $, $ 3^2 = 9 $, $ 4^2 = 16 $, $ 5^2 = 25 $, etc. The more you practice, the faster you'll recognize them!

Q: What if the number under the square root isn't a perfect square?

If it's not a perfect square (like √15), you either estimate the answer or leave it as is. For now, focus on perfect squares like 1, 4, 9, 16, 25, 36, 49, 64, 81, 100.

Q: Is there a trick to check my square root answers quickly?

Yes! Simply square your answer. If you think √16 = 4, check: $ 4 \times 4 = 16 $ ✓. If it matches the original number under the square root, you're correct!

Q: Can square roots ever be fractions or decimals?

Absolutely! For example, $ \sqrt{\frac{1}{4}} = \frac{1}{2} $ and √2 ≈ 1.414. But start with perfect squares first - they always give you nice whole number answers.

Perfect Square Roots with Basic Integers

$\sqrt{16}=$

❤️ 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

00:04 The square root of any number (X) squared, the root cancels the square

00:13 We'll break down 16 to 4 squared

00:20 We'll use this formula in our exercise

00:30 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

$\sqrt{16}=$

Step-by-step solution

To determine the square root of 16, follow these steps:

Identify that we are looking for the square root of 16, which is a number that, when multiplied by itself, equals 16.
Recall the basic property of perfect squares: $4 \times 4 = 16$ .
Thus, the square root of 16 is 4.

Hence, the solution to the problem is the principal square root, which is $4$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Definition: Square root finds the number that multiplies itself
Technique: Recognize that $4 \times 4 = 16$
Check: Verify by squaring your answer: $4^2 = 16$ ✓

Common Mistakes

Avoid these frequent errors

Confusing square root with half the number
Don't think √16 = 8 (half of 16) = wrong answer! Square root means finding what number times itself equals 16, not dividing by 2. Always ask: what number squared gives me 16?

Practice Quiz

Test your knowledge with interactive questions

$\sqrt{100}=$

FAQ

Everything you need to know about this question

Why isn't the answer -4 since (-4) × (-4) = 16?

Great observation! While both 4 and -4 when squared equal 16, the square root symbol $\sqrt{}$ always means the positive (principal) square root. So $\sqrt{16} = 4$ only.

How do I remember which numbers are perfect squares?

Practice the multiplication tables! Know that $1^2 = 1$ , $2^2 = 4$ , $3^2 = 9$ , $4^2 = 16$ , $5^2 = 25$ , etc. The more you practice, the faster you'll recognize them!

What if the number under the square root isn't a perfect square?

If it's not a perfect square (like √15), you either estimate the answer or leave it as is. For now, focus on perfect squares like 1, 4, 9, 16, 25, 36, 49, 64, 81, 100.

Is there a trick to check my square root answers quickly?

Yes! Simply square your answer. If you think √16 = 4, check: $4 \times 4 = 16$ ✓. If it matches the original number under the square root, you're correct!

Can square roots ever be fractions or decimals?

Absolutely! For example, $\sqrt{\frac{1}{4}} = \frac{1}{2}$ and √2 ≈ 1.414. But start with perfect squares first - they always give you nice whole number answers.

🌟 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