Calculate Side Length: Finding Square Root of Area 16

Square Root Applications with Perfect Squares

How long are the sides of a square that has an area of 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
00:05 Let's find the side of the square.
00:08 We use the formula for the area of a square, which is side times si de.
00:15 Now, substitute the given values and solve for the side.
00:23 Take the square root of your answer.
00:29 Remember, there are always two solutions when taking a square ro ot.
00:34 But, the side length must be greater than zero.
00:39 And that's how we find the side of the square.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

How long are the sides of a square that has an area of 16?

2

Step-by-step solution

We need to determine the side length of a square whose area is 16.

  • Step 1: Set up the equation using the area formula for a square, A=s2 A = s^2 . Given the area A=16 A = 16 , we have:
    s2=16 s^2 = 16
  • Step 2: Solve for s s by taking the square root of both sides:
    s=16 s = \sqrt{16}
  • Step 3: Calculate the square root:
    s=4 s = 4

Since a side length cannot be negative, we take only the positive square root. Therefore, the side length of the square is 4 4 , which corresponds to choice 4.

3

Final Answer

4

Key Points to Remember

Essential concepts to master this topic
  • Formula: Area of square equals side length squared: A=s2 A = s^2
  • Technique: Take square root of area: s=16=4 s = \sqrt{16} = 4
  • Check: Verify by squaring answer: 42=16 4^2 = 16 matches given area ✓

Common Mistakes

Avoid these frequent errors
  • Taking negative square root or forgetting it exists
    Don't think 16=−4 \sqrt{16} = -4 or ignore the negative solution = impossible side length! Side lengths must be positive distances in geometry problems. Always take only the positive square root for measurements.

Practice Quiz

Test your knowledge with interactive questions

Look at the square below:

555

What is the area of the square equivalent to?

FAQ

Everything you need to know about this question

Why can't the side length be negative 4?

+

Great question! While (−4)2=16 (-4)^2 = 16 mathematically, side lengths represent physical distances which are always positive. In geometry, we only use positive values for measurements.

How do I know 16 is a perfect square?

+

Perfect squares are numbers like 1, 4, 9, 16, 25... that result from squaring whole numbers. Since 42=16 4^2 = 16 , we know 16 is a perfect square with exact square root 4.

What if the area wasn't a perfect square?

+

You'd still take the square root, but it might be a decimal or irrational number. For example, if area = 15, then s=15≈3.87 s = \sqrt{15} \approx 3.87 .

Do I always use the area formula for squares?

+

Yes! For any square problem involving area and side length, always start with A=s2 A = s^2 . This formula connects the two measurements directly.

How can I remember which operation to use?

+

Think: "Area to side = square root, side to area = square." Going from area (16) to side length means taking 16 \sqrt{16} !

🌟 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

More Questions

Click on any question to see the complete solution with step-by-step explanations

Square Roots

Calculate Square Root: Finding Side Length When Area = 100
Click to solve
Solve Square Root Addition: √16 + √4 Step by Step
Click to solve

Area of the Square