Calculate Side Length: Finding Square Root of Area 9

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

Because area is calculated by multiplying side × side, so to find the side length, you need to reverse this operation using the square root.

Q: How do I remember the square area formula?

Think of it as side × side = area. If you know the area, you need to find what number times itself gives that area - that's the square root!

Q: Can the side length ever be negative?

No! Side lengths represent distance, which is always positive. Even though $ (-3)^2 = 9 $, we only use the positive square root for geometry.

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

Area is the space inside (measured in square units), while perimeter is the distance around the edge. For this square: area = 9, perimeter = 4 × 3 = 12.

Square Root Calculation with Perfect Squares

Below is a square with an area of 9.

How long are the sides of the square?

❤️ 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 Find the side of the square

00:03 We'll use the formula for calculating the area of a square (side squared)

00:09 We'll substitute appropriate values and solve for the side

00:17 We'll extract the root

00:26 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

Below is a square with an area of 9.

How long are the sides of the square?

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:

$9=a^2$

We extract the root:

$\sqrt{9}=L$

$3=L$

Final Answer

$3$

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: $\sqrt{9} = 3$
Check: Verify by squaring answer: $3^2 = 9$ matches given area ✓

Common Mistakes

Avoid these frequent errors

Confusing area with side length
Don't use 9 as the side length directly = perimeter of 36 instead of correct 12! The area (9) is not the same as the side length. 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 need to take the square root of the area?

Because area is calculated by multiplying side × side, so to find the side length, you need to reverse this operation using the square root.

What if the area isn't a perfect square like 9?

You can still find the square root! For example, if area = 10, then side length = $\sqrt{10} \approx 3.16$ . Use a calculator for non-perfect squares.

How do I remember the square area formula?

Think of it as side × side = area. If you know the area, you need to find what number times itself gives that area - that's the square root!

Can the side length ever be negative?

No! Side lengths represent distance, which is always positive. Even though $(-3)^2 = 9$ , we only use the positive square root for geometry.

What's the difference between area and perimeter?

Area is the space inside (measured in square units), while perimeter is the distance around the edge. For this square: area = 9, perimeter = 4 × 3 = 12.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Square for 9th Grade 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