Find the Side Length of a Square with Area 49: Square Root Problem

Q: What exactly is a square root?

A square root is the number that, when multiplied by itself, gives you the original number. So $ \sqrt{49} = 7 $ because 7 × 7 = 49.

Q: How do I remember perfect squares?

Practice memorizing common perfect squares: 1² = 1, 2² = 4, 3² = 9, 4² = 16, 5² = 25, 6² = 36, 7² = 49, 8² = 64, 9² = 81, 10² = 100. These come up frequently!

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

If the area doesn't have a whole number square root, you might need to use a calculator or leave your answer as $ \sqrt{number} $. But in most problems like this, they use perfect squares.

Q: Why does Area = side² for squares?

Because a square has equal sides, the area is side × side = side². It's like making a grid: if each side is 7 units, you have 7 rows of 7 squares each = 49 total squares.

Q: Can the side length be negative?

No! Side lengths represent distance and must be positive. Even though $ (-7)² = 49 $, we only use the positive square root for measurements.

Square Root Applications with Perfect Squares

A square has an area of 49.

How long are its sides?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's find the side of the square.

00:07 We use the formula: Area equals side times side.

00:12 Substitute the numbers you have to find the side.

00:18 Next, take the square root.

00:22 Remember, square roots can give two answers.

00:27 But the side length must be more than zero.

00:31 And that's 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 49.

How long are its sides?

Step-by-step solution

Since the area of the square is equal to the side raised to the 2nd power, we use the formula to find the side:

$49=a^2$

$a=7$

Final Answer

$7$

Key Points to Remember

Essential concepts to master this topic

Area Formula: For squares, Area = side × side = side²
Technique: Find square root of area: $\sqrt{49} = 7$
Check: Verify by squaring answer: $7² = 7 × 7 = 49$ ✓

Common Mistakes

Avoid these frequent errors

Confusing area with side length
Don't think the area 49 IS the side length = wrong answer of 49! The area is the side multiplied by itself, so you need to find what number times itself equals 49. 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 equivalent to?

FAQ

Everything you need to know about this question

What exactly is a square root?

A square root is the number that, when multiplied by itself, gives you the original number. So $\sqrt{49} = 7$ because 7 × 7 = 49.

How do I remember perfect squares?

Practice memorizing common perfect squares: 1² = 1, 2² = 4, 3² = 9, 4² = 16, 5² = 25, 6² = 36, 7² = 49, 8² = 64, 9² = 81, 10² = 100. These come up frequently!

What if the area isn't a perfect square?

If the area doesn't have a whole number square root, you might need to use a calculator or leave your answer as $\sqrt{number}$ . But in most problems like this, they use perfect squares.

Why does Area = side² for squares?

Because a square has equal sides, the area is side × side = side². It's like making a grid: if each side is 7 units, you have 7 rows of 7 squares each = 49 total squares.

Can the side length be negative?

No! Side lengths represent distance and must be positive. Even though $(-7)² = 49$ , we only use the positive square root for measurements.

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