Square Root Problem: Finding Side Length When Area is 169

Q: How do I know if 169 is a perfect square?

A perfect square has a whole number as its square root. You can check by testing numbers: 10² = 100, 11² = 121, 12² = 144, 13² = 169. Since 13² gives exactly 169, it's a perfect square!

Q: Why can't the side length be negative?

In geometry, lengths are always positive numbers. Even though (-13)² = 169 mathematically, a square can't have a negative side length in the real world!

Q: How do I remember the area formula for squares?

Think of it as side × side = s². A square with side 5 has area 5 × 5 = 25. The formula A = s² just shows this multiplication in shorter form.

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

Area measures the space inside (s²), while perimeter measures the distance around the outside (4s). For our square: area = 169, perimeter = 4 × 13 = 52.

Square Area with Perfect Square Root

A square has an area of 169.

How long are its sides?

❤️ 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

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

00:08 Remember, the area of a square is found by squaring the length of one side.

00:14 Now, substitute the given area and solve for the side length.

00:19 Take the square root of the area to find the side length.

00:28 And that's how you find the side of the square!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

A square has an area of 169.

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.

We substitute the data into the formula:

$169=L^2$

We calculate the root:

$\sqrt{169}=a$

$L=13$

Final Answer

$13$

Key Points to Remember

Essential concepts to master this topic

Formula: Area of square equals side length squared (A = s²)
Technique: Find square root of area: √169 = 13
Check: Verify by squaring the answer: 13² = 169 ✓

Common Mistakes

Avoid these frequent errors

Confusing area with perimeter formula
Don't divide 169 by 4 to get 42.25! This treats area like perimeter and gives completely wrong side lengths. Always remember that area equals side squared, so you must take the square root of the area.

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

How do I know if 169 is a perfect square?

A perfect square has a whole number as its square root. You can check by testing numbers: 10² = 100, 11² = 121, 12² = 144, 13² = 169. Since 13² gives exactly 169, it's a perfect square!

What if the area wasn't a perfect square?

You'd still take the square root, but the answer might be a decimal. For example, if area = 170, then side length = √170 ≈ 13.04. Use a calculator for non-perfect squares.

Why can't the side length be negative?

In geometry, lengths are always positive numbers. Even though (-13)² = 169 mathematically, a square can't have a negative side length in the real world!

How do I remember the area formula for squares?

Think of it as side × side = s². A square with side 5 has area 5 × 5 = 25. The formula A = s² just shows this multiplication in shorter form.

What's the difference between area and perimeter?

Area measures the space inside (s²), while perimeter measures the distance around the outside (4s). For our square: area = 169, perimeter = 4 × 13 = 52.

🌟 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