Calculate the Square Root: Finding √441 Step by Step

Q: How do I know if 441 is a perfect square?

Try to find a whole number that when multiplied by itself gives 441. Since 21 × 21 = 441, it's a perfect square! If no whole number works, you'd need to estimate or use a calculator.

Q: Why are the other answer choices wrong?

Options like 20 + √41 are not simplified and don't equal a clean whole number. Since 441 is a perfect square, the answer must be a simple whole number: 21.

Q: How can I check my square root answer quickly?

Simply square your answer! If you think √441 = 21, calculate 21² = 441. If it matches the original number under the radical, you're correct!

Q: What's the fastest way to calculate 21×21?

Method 1: 21 × 21 = (20+1)² = 20² + 2(20)(1) + 1² = 400 + 40 + 1 = 441Method 2: 21 × 21 = 21 × 20 + 21 × 1 = 420 + 21 = 441

Perfect Squares with Mental Calculation

$\sqrt{441}=$

❤️ 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

00:03 Let's break down 441 to 21 squared

00:08 The root and square cancel each other out, 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

$\sqrt{441}=$

Step-by-step solution

The root of 441 is 21.

$21\times21=$

$21\times20+21=$

$420+21=441$

Final Answer

$21$

Key Points to Remember

Essential concepts to master this topic

Perfect Square: 441 is 21² because 21×21 equals 441
Technique: Break down 21×21 = 21×20 + 21 = 420 + 21
Check: Verify that 21² = 441 by multiplying 21×21 ✓

Common Mistakes

Avoid these frequent errors

Confusing square root with squaring
Don't think √441 means 441² = 194,481! This confuses the operation and gives a massive wrong answer. Always remember that square root asks 'what number times itself gives 441?'

Practice Quiz

Test your knowledge with interactive questions

$\sqrt{100}=$

FAQ

Everything you need to know about this question

How do I know if 441 is a perfect square?

Try to find a whole number that when multiplied by itself gives 441. Since 21 × 21 = 441, it's a perfect square! If no whole number works, you'd need to estimate or use a calculator.

What if I don't remember that 21² = 441?

Start by testing numbers around 20. Since 20² = 400, try 21: $21 \times 21 = 21 \times 20 + 21 = 420 + 21 = 441$ . Breaking it down makes it easier!

Why are the other answer choices wrong?

Options like 20 + √41 are not simplified and don't equal a clean whole number. Since 441 is a perfect square, the answer must be a simple whole number: 21.

How can I check my square root answer quickly?

Simply square your answer! If you think √441 = 21, calculate 21² = 441. If it matches the original number under the radical, you're correct!

What's the fastest way to calculate 21×21?

Method 1: 21 × 21 = (20+1)² = 20² + 2(20)(1) + 1² = 400 + 40 + 1 = 441
Method 2: 21 × 21 = 21 × 20 + 21 × 1 = 420 + 21 = 441

🌟 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