Calculate Side Length: Finding Square Root of 16 Square Units

Q: Why do I take the square root instead of dividing by 4?

Because area measures square units, not linear units! If each side is 4, then area = 4 × 4 = 16. To reverse this, you need the square root, not division.

Q: How do I remember the difference between area and perimeter?

Area fills the inside (square units), while perimeter goes around the edge (linear units). Area uses multiplication, perimeter uses addition!

Q: Can a square root be negative?

In geometry problems about length, we only use the positive square root because lengths can't be negative. So $ \sqrt{16} = 4 $, not -4.

Q: What's the easiest way to check my work?

Square your answer! If you think the side is 4, calculate $ 4^2 = 16 $. If this equals the given area, you're right!

Square Root Operations with Perfect Squares

A square has an area of 16.

How long are its sides?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the side of the square

00:03 Use the formula for calculating the area of a square (side squared)

00:11 Substitute appropriate values and solve to find the side

00:17 Take the square root

00:25 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

A square has an area of 16.

How long are its sides?

Step-by-step solution

Remember that the area of a square is equal to the side of the square squared.

The formula for the area of a square is:

$S=a^2$

Calculate the area of the square:

$16=a^2$

Calculate the square root:

$\sqrt{16}=a$

$4=a$

Final Answer

$4$

Key Points to Remember

Essential concepts to master this topic

Area Formula: Area of square equals side length squared
Technique: Use inverse operation: if $a^2 = 16$ , then $a = \sqrt{16}$
Check: Verify by squaring your answer: $4^2 = 16$ ✓

Common Mistakes

Avoid these frequent errors

Confusing area with perimeter calculations
Don't divide 16 by 4 to get side length = 4! This treats area like perimeter and gives the wrong reasoning. Area is side × side, not 4 × side. Always take the square root of the area to find side length.

Practice Quiz

Test your knowledge with interactive questions

Look at the square below:

What is the area of the square?

FAQ

Everything you need to know about this question

Why do I take the square root instead of dividing by 4?

Because area measures square units, not linear units! If each side is 4, then area = 4 × 4 = 16. To reverse this, you need the square root, not division.

What if the area wasn't a perfect square like 16?

You'd still take the square root, but it might not be a whole number. For example, if area = 18, then side length = $\sqrt{18} \approx 4.24$ units.

How do I remember the difference between area and perimeter?

Area fills the inside (square units), while perimeter goes around the edge (linear units). Area uses multiplication, perimeter uses addition!

Can a square root be negative?

In geometry problems about length, we only use the positive square root because lengths can't be negative. So $\sqrt{16} = 4$ , not -4.

What's the easiest way to check my work?

Square your answer! If you think the side is 4, calculate $4^2 = 16$ . If this equals the given area, you're right!

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