Calculate Side Length: Finding Square Dimensions When Area = 900

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

Because the area formula is $ A = s^2 $, where s is the side length. To find s, we need to 'undo' the squaring by taking the square root of both sides.

Q: How do I know 30 is the square root of 900?

You can check by multiplying: $ 30 \times 30 = 900 $. Also, memorizing perfect squares like 900 = 30² helps you recognize them quickly!

Q: Can a square have negative side lengths?

No! Side lengths are always positive measurements. Even though $ (-30)^2 = 900 $, we only use the positive square root for real measurements.

Q: How is this different from finding the area?

Finding area means squaring the side length: $ s^2 $. Finding side length means taking the square root of the area: $ \sqrt{A} $. They're opposite operations!

Square Root Applications with Perfect Squares

A square has an area of 900.

Ho 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

00:18 We'll take the square root

00:21 When taking a square root there are always 2 solutions

00:25 The length of the side must be greater than 0

00:31 And this is the solution to 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 900.

Ho 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:

$900=L^2$

We extract the root:

$\sqrt{900}=L$

$L=30$

Final Answer

$30$

Key Points to Remember

Essential concepts to master this topic

Formula: Area of square equals side length squared ( $A = s^2$ )
Technique: Find square root of area: $\sqrt{900} = 30$
Check: Verify by squaring: $30^2 = 30 \times 30 = 900$ ✓

Common Mistakes

Avoid these frequent errors

Dividing area by 2 instead of taking square root
Don't divide 900 ÷ 2 = 450! This confuses area formulas and gives a completely wrong side length. The area formula is s², not 2s. 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 $A = s^2$ , where s is the side length. To find s, we need to 'undo' the squaring by taking the square root of both sides.

How do I know 30 is the square root of 900?

You can check by multiplying: $30 \times 30 = 900$ . Also, memorizing perfect squares like 900 = 30² helps you recognize them quickly!

What if the area isn't a perfect square?

Then your answer will include a square root symbol. For example, if area = 50, then side length = $\sqrt{50}$ , which you can simplify to $5\sqrt{2}$ .

Can a square have negative side lengths?

No! Side lengths are always positive measurements. Even though $(-30)^2 = 900$ , we only use the positive square root for real measurements.

How is this different from finding the area?

Finding area means squaring the side length: $s^2$ . Finding side length means taking the square root of the area: $\sqrt{A}$ . They're opposite operations!

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