Find the Side Length of a Square with Area 25: Basic Geometry Problem

Q: Why do I need to find the square root of 25?

Because area = side × side, so if area is 25, then side × side = 25. The square root 'undoes' the squaring to find the original side length.

Q: How do I remember which formula to use?

Think visually! Area covers the inside of the square (length × width = side × side). Perimeter goes around the outside (4 × side length).

Q: Can the side length ever be negative?

No! Side lengths represent distance, which is always positive. Even though $ (-5)^2 = 25 $, we only use the positive square root for measurements.

Q: What's the difference between 5² and √25?

$ 5^2 $ means 5 × 5 = 25 (squaring). $ \sqrt{25} $ means 'what number times itself equals 25?' = 5 (square root). They're opposite operations!

Square Area with Perfect Square Numbers

A square has an area of 25.

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)

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

00:15 We'll extract the root

00:20 When extracting a root there are always 2 solutions

00:25 The side length must be greater than 0

00:30 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 25.

How long are its sides?

Step-by-step solution

Remember that the area of a square is equal to the side of the square raised to the 2nd power.

Now, we replace the data in the formula:

$25=L^2$

We extract the square root:

$\sqrt{25}=L$

$L=5$

Final Answer

$5$

Key Points to Remember

Essential concepts to master this topic

Area Formula: Square area equals side length squared (A = s²)
Technique: Find square root of area: √25 = 5
Check: Verify by squaring the answer: 5² = 25 ✓

Common Mistakes

Avoid these frequent errors

Confusing area and perimeter formulas
Don't divide the area by 4 thinking it's perimeter = 6.25! Area uses s², not 4s. Always remember area = side × side, so 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 find the square root of 25?

Because area = side × side, so if area is 25, then side × side = 25. The square root 'undoes' the squaring to find the original side length.

What if the area isn't a perfect square like 25?

You'll still take the square root, but the answer might be a decimal or need to stay as $\sqrt{n}$ . For example, if area = 20, then side = $\sqrt{20}$ ≈ 4.47.

How do I remember which formula to use?

Think visually! Area covers the inside of the square (length × width = side × side). Perimeter goes around the outside (4 × side length).

Can the side length ever be negative?

No! Side lengths represent distance, which is always positive. Even though $(-5)^2 = 25$ , we only use the positive square root for measurements.

What's the difference between 5² and √25?

$5^2$ means 5 × 5 = 25 (squaring). $\sqrt{25}$ means 'what number times itself equals 25?' = 5 (square root). They're opposite operations!

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