Calculate Side Length: Finding Square Root of Area 4

Q: Why do I take the square root of the area?

Because the area formula is $ A = L^2 $, where L is squared. To find L, you need to undo the squaring operation by taking the square root of both sides.

Q: Can the side length be negative?

No! Side lengths represent physical distances, which are always positive. Even though $ (-2)^2 = 4 $, we only use the positive square root for geometry problems.

Q: How do I remember which formula to use?

Think of it this way: Area covers the inside of the square, so you multiply length × width. For squares, length = width, so $ A = L \times L = L^2 $!

Q: What's the difference between area and perimeter?

Area measures the space inside (uses $ L^2 $), while perimeter measures the distance around the edge (uses $ 4L $ for squares).

Square Root Calculation with Area Formulas

A square has an area equal to 4.

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 We'll use the formula for calculating the area of a square (side squared)

00:07 We'll substitute appropriate values and solve for the side

00:15 We'll extract the root

00:23 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 equal to 4.

How long are its sides?

Step-by-step solution

Remember that the area of the square is equal to the side of the square raised to the second power.

The formula for the area of the square is:

$A=L^2$

We calculate the area of the square:

$4=L^2$

We extract the square root:

$\sqrt{4}=L$

$2=L$

Final Answer

$2$

Key Points to Remember

Essential concepts to master this topic

Formula: Area of square equals side length squared: $A = L^2$
Technique: Find square root of area: $\sqrt{4} = 2$
Check: Verify by squaring answer: $2^2 = 4$ matches given area ✓

Common Mistakes

Avoid these frequent errors

Confusing area with side length
Don't think the side length equals 4 because area is 4 = wrong answer! Area is side squared, not just the side itself. Always take the square root of the area to find the 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 of the area?

Because the area formula is $A = L^2$ , where L is squared. To find L, you need to undo the squaring operation by taking the square root of both sides.

What if the area isn't a perfect square?

You'll get a decimal or irrational number! For example, if area is 5, then side length is $\sqrt{5} \approx 2.24$ . Use a calculator when needed.

Can the side length be negative?

No! Side lengths represent physical distances, which are always positive. Even though $(-2)^2 = 4$ , we only use the positive square root for geometry problems.

How do I remember which formula to use?

Think of it this way: Area covers the inside of the square, so you multiply length × width. For squares, length = width, so $A = L \times L = L^2$ !

What's the difference between area and perimeter?

Area measures the space inside (uses $L^2$ ), while perimeter measures the distance around the edge (uses $4L$ for squares).

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