Square Root Problem: Finding Side Length When Area = 121

Q: How do I know 121 is a perfect square?

A perfect square is a number that equals another whole number times itself. Since $ 11 \times 11 = 121 $, we know 121 is a perfect square with square root 11.

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

You'd still take the square root, but you might get a decimal or need to leave it as a square root symbol. For example, if area = 50, then side length = $ \sqrt{50} \approx 7.07 $.

Q: Why do we only use the positive square root?

Since we're measuring the length of a side, it must be positive! Negative lengths don't make sense in geometry, even though $ (-11)^2 = 121 $ too.

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

Think "side squared" - if each side is 11 units, imagine making an 11×11 grid of unit squares. You'd have $ 11^2 = 121 $ total squares!

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

Area: Space inside = side × side = $ s^2 $Perimeter: Distance around = 4 × side = 4sDon't mix them up!

Square Root Operations with Perfect Squares

A square has an area of 121.

How long are it 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

00:12 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 121.

How long are it sides?

Step-by-step solution

Remember that the area of the square is equal to the side of the square raised to the 2nd power.

Now we replace the data in the formula:

$121=L^2$

We extract the root:

$\sqrt{121}=L$

$L=11$

Final Answer

$11$

Key Points to Remember

Essential concepts to master this topic

Area Formula: Area of square equals side length squared
Technique: Take square root of area: $\sqrt{121} = 11$
Check: Verify by squaring: $11^2 = 11 \times 11 = 121$ ✓

Common Mistakes

Avoid these frequent errors

Confusing area formula with perimeter formula
Don't use Area = 4 × side length = wrong formula for squares! This gives you the perimeter, not area, leading to answers like 30.25 instead of 11. Always remember Area = side² for squares.

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 121 is a perfect square?

A perfect square is a number that equals another whole number times itself. Since $11 \times 11 = 121$ , we know 121 is a perfect square with square root 11.

What if the area wasn't a perfect square?

You'd still take the square root, but you might get a decimal or need to leave it as a square root symbol. For example, if area = 50, then side length = $\sqrt{50} \approx 7.07$ .

Why do we only use the positive square root?

Since we're measuring the length of a side, it must be positive! Negative lengths don't make sense in geometry, even though $(-11)^2 = 121$ too.

How can I remember the area formula for squares?

Think "side squared" - if each side is 11 units, imagine making an 11×11 grid of unit squares. You'd have $11^2 = 121$ total squares!

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

Area: Space inside = side × side = $s^2$
Perimeter: Distance around = 4 × side = 4s

Don't mix them up!

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