Calculate Side Length: Finding Square Root of Area 36

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

Because area of a square is side × side, which equals $ s^2 $. To find the side length, you need to reverse this operation by taking the square root!

Q: What if the area isn't a perfect square?

You'll get a decimal or need to leave your answer as $ \sqrt{\text{number}} $. For example, if area is 50, the side length is $ \sqrt{50} $ or about 7.07.

Q: How do I remember which formula to use?

Key tip: If you're given area and need side length, use $ \sqrt{\text{area}} $. If you're given side length and need area, use $ \text{side}^2 $.

Q: Can the side length be negative?

No! Side lengths represent distance, which is always positive. Even though $ (-6)^2 = 36 $, we only use the positive square root for measurements.

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

Area is the space inside (measured in square units like cm²). Perimeter is the distance around the outside (measured in regular units like cm). Don't mix up their formulas!

Square Area with Side Length Calculation

A square has an area of 36.

How long are its sides?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's find the length of one side of the square.

00:08 Remember, the area of a square equals the side length times the side length.

00:14 Now, plug in the known numbers, and solve for the side length.

00:20 Great, now take the square root to find the side.

00:28 And that, my friends, is how you solve the problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

A square has an area of 36.

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:

$S=a^2$

Let's calculate the area of the square:

$36=a^2$

Let's take the square root:

$\sqrt{36}=a$

$6=a$

Final Answer

$6$

Key Points to Remember

Essential concepts to master this topic

Area Formula: For squares, area equals side length squared: $A = s^2$
Technique: Take square root of area: $\sqrt{36} = 6$
Check: Verify by squaring answer: $6^2 = 36$ ✓

Common Mistakes

Avoid these frequent errors

Confusing area with perimeter formulas
Don't use $36 ÷ 4 = 9$ thinking about perimeter! This gives the wrong side length because area and perimeter are completely different measurements. Always use $\sqrt{\text{area}}$ to find side length from area.

Practice Quiz

Test your knowledge with interactive questions

Look at the square below:

What is the area of the square equivalent to?

FAQ

Everything you need to know about this question

Why do I take the square root of the area?

Because area of a square is side × side, which equals $s^2$ . To find the side length, you need to reverse this operation by taking the square root!

What if the area isn't a perfect square?

You'll get a decimal or need to leave your answer as $\sqrt{\text{number}}$ . For example, if area is 50, the side length is $\sqrt{50}$ or about 7.07.

How do I remember which formula to use?

Key tip: If you're given area and need side length, use $\sqrt{\text{area}}$ . If you're given side length and need area, use $\text{side}^2$ .

Can the side length be negative?

No! Side lengths represent distance, which is always positive. Even though $(-6)^2 = 36$ , we only use the positive square root for measurements.

What's the difference between area and perimeter?

Area is the space inside (measured in square units like cm²). Perimeter is the distance around the outside (measured in regular units like cm). Don't mix up their formulas!

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