Square Root Calculation: Finding Side Length of a 400-Unit² Square

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

Because area equals side × side, not side × 2! To 'undo' squaring, you need the square root, which is the opposite operation of squaring.

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

You'll get a decimal or irrational number. For example, if area = 50, then side length = $ \sqrt{50} \approx 7.07 $ units.

Q: How do I know 400 is a perfect square?

Perfect squares end in 0, 1, 4, 5, 6, or 9. Since 400 ends in 00, it could be perfect. Try: $ 20^2 = 400 $ ✓

Q: Can a square have negative side length?

No! Side lengths are always positive distances. Even though $ (-20)^2 = 400 $, we only use the positive square root for measurements.

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

Area: Space inside = side²Perimeter: Distance around = 4 × sideFor this square: Area = 400, Perimeter = 4 × 20 = 80

Square Root Operations with Perfect Squares

A square has an area of 400.

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

00:05 We'll use the formula for calculating the area of a square (side squared)

00:11 We'll substitute appropriate values and solve for the side

00:16 Extract the root

00:21 When extracting a root there are always 2 solutions

00:26 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 400.

How long are its sides?

Step-by-step solution

The area of the square is equal to the length of the square raised to the second power.

That is:

$A=L^2$

Since we know that the area of the square is equal to 400, we perform the formula as follows:

$400=L^2$

We solve the square root:

$\sqrt{400}=L$

$L=20$

The side of the square is equal to 20.

Final Answer

$20$

Key Points to Remember

Essential concepts to master this topic

Formula: Area of square equals side length squared (A = L²)
Technique: Take square root of both sides: √400 = √L²
Check: Verify by squaring answer: 20² = 400 ✓

Common Mistakes

Avoid these frequent errors

Dividing area by 2 instead of taking square root
Don't divide 400 by 2 to get 200 = wrong side length! This confuses area with perimeter formulas. 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 instead of dividing?

Because area equals side × side, not side × 2! To 'undo' squaring, you need the square root, which is the opposite operation of squaring.

What if the area isn't a perfect square?

You'll get a decimal or irrational number. For example, if area = 50, then side length = $\sqrt{50} \approx 7.07$ units.

How do I know 400 is a perfect square?

Perfect squares end in 0, 1, 4, 5, 6, or 9. Since 400 ends in 00, it could be perfect. Try: $20^2 = 400$ ✓

Can a square have negative side length?

No! Side lengths are always positive distances. Even though $(-20)^2 = 400$ , we only use the positive square root for measurements.

What's the difference between area and perimeter of a square?

Area: Space inside = side²
Perimeter: Distance around = 4 × side

For this square: Area = 400, Perimeter = 4 × 20 = 80

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