Calculate Square Side Length: Finding Dimensions When Area = 64

Q: Why do we use square root instead of just dividing?

Because area comes from multiplying side × side. To reverse multiplication, we use square root, not division. Think: if $ s \times s = 64 $, then $ s = \sqrt{64} $.

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

Remember: "Side times Side" or $ s^2 $. A square has equal sides, so you multiply the same length twice. That's why we write it as side squared.

Q: What if I get a negative number under the square root?

That's impossible with area problems! Area is always positive, so you'll never have negative numbers. If you see a negative, check your setup.

Q: Can I use this method for rectangles too?

No! Rectangles have different length and width, so the formula is $ A = l \times w $. This square root method only works when all sides are equal.

Square Area Formula with Perfect Squares

A square has an area of 64.

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

00:03 Use the formula for calculating the area of a square (side squared)

00:08 Substitute appropriate values and solve to find the side

00:13 Extract the root

00:22 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 64.

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 second power.

Now we substitute the data into the formula:

$64=L^2$

Then, we calculate the square root:

$\sqrt{64}=L$

$L=8$

Final Answer

$8$

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: $\sqrt{64} = 8$
Check: Verify by squaring answer: $8^2 = 64$ matches given area ✓

Common Mistakes

Avoid these frequent errors

Adding or dividing instead of taking square root
Don't divide 64 by 4 to get 16 or add numbers randomly = wrong side length! Area requires squaring, so finding the side requires the reverse operation. 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

What if the area isn't a perfect square like 64?

You can still take the square root! For non-perfect squares like 50, the answer would be $\sqrt{50}$ or approximately 7.07. Use a calculator for decimal approximations.

Why do we use square root instead of just dividing?

Because area comes from multiplying side × side. To reverse multiplication, we use square root, not division. Think: if $s \times s = 64$ , then $s = \sqrt{64}$ .

How do I remember the area formula for squares?

Remember: "Side times Side" or $s^2$ . A square has equal sides, so you multiply the same length twice. That's why we write it as side squared.

What if I get a negative number under the square root?

That's impossible with area problems! Area is always positive, so you'll never have negative numbers. If you see a negative, check your setup.

Can I use this method for rectangles too?

No! Rectangles have different length and width, so the formula is $A = l \times w$ . This square root method only works when all sides are equal.

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