Calculate Square Side Length: Finding x When Area = 144

Q: Why do we take the square root instead of dividing?

Because area equals side × side, not side × 4! The formula is $ \text{Area} = s^2 $, so to find s, we need the inverse operation of squaring, which is taking the square root.

Q: What if the area isn't a perfect square like 144?

You'll get an irrational number like $ \sqrt{50} $. You can leave it in square root form or use a calculator to find the decimal approximation!

Q: How do I know if 144 is a perfect square?

Think of multiplication tables: $ 12 \times 12 = 144 $! Perfect squares are numbers you get when you multiply a whole number by itself. Practice memorizing common ones like $ 1^2, 2^2, 3^2... 12^2 $.

Q: Can a square have negative side length?

No! In geometry, lengths are always positive. Even though $ (-12)^2 = 144 $ mathematically, we only consider the positive square root for real-world measurements.

Q: Why is the answer choice √144 instead of just 12?

The choice $ \sqrt{144} $ shows the process you need to solve the problem! It demonstrates that you understand taking the square root is the correct operation, even though it equals 12.

Area Formula with Square Root Operations

Calculate the length of the sides of the square given that its area is equal to 144.

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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 to find the side

00:18 Take the square root

00:22 When taking a square root there are always 2 solutions

00:29 The length of the side must be greater than 0

00:34 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

Calculate the length of the sides of the square given that its area is equal to 144.

Step-by-step solution

To calculate the length of the sides of a square given that its area is 144, we follow these steps:

The problem gives us that the area of the square is 144. We are looking for the side length ( $s$ ) of the square.
We use the formula for the area of a square: $\text{Area} = \text{side}^2$ . Substituting the given area, we have $144 = s^2$ .
We solve for $s$ by taking the square root of both sides: $s = \sqrt{144}$ .
Calculating $\sqrt{144}$ , we find that $s = 12$ .

Therefore, the length of the sides of the square is 12.

This corresponds to choice 4: $\sqrt{144}$ , which emphasizes using the square root operation. However, the final calculation confirms that $s = 12$ .

Final Answer

$\sqrt{144}$

Key Points to Remember

Essential concepts to master this topic

Formula: Area of square equals side length squared
Technique: Take square root of both sides: $s = \sqrt{144} = 12$
Check: Verify by squaring your answer: $12^2 = 144$ ✓

Common Mistakes

Avoid these frequent errors

Adding or dividing the area instead of taking square root
Don't divide 144 by 4 or try adding numbers = wrong side length! The area formula is $s^2 = 144$ , not $s \times 4 = 144$ . Always take the square root to reverse the squaring operation.

Practice Quiz

Test your knowledge with interactive questions

$\sqrt{100}=$

FAQ

Everything you need to know about this question

Why do we take the square root instead of dividing?

Because area equals side × side, not side × 4! The formula is $\text{Area} = s^2$ , so to find s, we need the inverse operation of squaring, which is taking the square root.

What if the area isn't a perfect square like 144?

You'll get an irrational number like $\sqrt{50}$ . You can leave it in square root form or use a calculator to find the decimal approximation!

How do I know if 144 is a perfect square?

Think of multiplication tables: $12 \times 12 = 144$ ! Perfect squares are numbers you get when you multiply a whole number by itself. Practice memorizing common ones like $1^2, 2^2, 3^2... 12^2$ .

Can a square have negative side length?

No! In geometry, lengths are always positive. Even though $(-12)^2 = 144$ mathematically, we only consider the positive square root for real-world measurements.

Why is the answer choice √144 instead of just 12?

The choice $\sqrt{144}$ shows the process you need to solve the problem! It demonstrates that you understand taking the square root is the correct operation, even though it equals 12.

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Calculate Square Side Length: Finding x When Area = 144

Area Formula with Square Root Operations

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do we take the square root instead of dividing?

What if the area isn't a perfect square like 144?

How do I know if 144 is a perfect square?

Can a square have negative side length?

Why is the answer choice √144 instead of just 12?

🌟 Unlock Your Math Potential

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