Calculate Square Root: Finding Side Length When Area = 100

Square Root Calculation with Perfect Squares

How long are the sides of a square if its area is equal to 100?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:05 Let's find the length of the side of this square.
00:08 We'll use the formula for the area of a square, which is side, times side.
00:16 Next, we'll substitute the given area into the formula to solve for the side.
00:23 Now, take the square root of that number.
00:31 Remember, the square root gives us two possible answers.
00:37 Since a side length must be positive, we choose the positive number.
00:42 And that's how we find the side of the square!

Step-by-step written solution

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1

Understand the problem

How long are the sides of a square if its area is equal to 100?

2

Step-by-step solution

To determine the length of the sides of a square when the area is given, we proceed as follows:

  • Step 1: Recall the formula for the area of a square: Area=side2 \text{Area} = \text{side}^2 .
  • Step 2: We need to find the side length, so we rearrange the formula to solve for the side: side=Area \text{side} = \sqrt{\text{Area}} .
  • Step 3: Substitute the given area into the formula: side=100 \text{side} = \sqrt{100} .
  • Step 4: Calculate the square root: 100=10 \sqrt{100} = 10 .

Therefore, the length of each side of the square is 10 10 .

3

Final Answer

10

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: 100=10 \sqrt{100} = 10
  • Check: Verify by squaring answer: 102=100 10^2 = 100

Common Mistakes

Avoid these frequent errors
  • Confusing square root with division
    Don't divide the area by 2 to find the side length = wrong answer of 50! Division doesn't reverse squaring. 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:

555

What is the area of the square equivalent to?

FAQ

Everything you need to know about this question

What exactly is a square root?

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A square root is the number that, when multiplied by itself, gives you the original number. So 100=10 \sqrt{100} = 10 because 10×10=100 10 \times 10 = 100 .

How do I remember the area formula for a square?

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Think of it as side × side = side². Since all four sides of a square are equal, you're multiplying the same length twice!

What if the area isn't a perfect square like 100?

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You can still find the square root! For example, if area = 50, then side = 507.07 \sqrt{50} \approx 7.07 . Use a calculator for non-perfect squares.

Why do we only consider the positive square root?

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Length measurements are always positive! While (10)2=100 (-10)^2 = 100 too, a side length of -10 doesn't make sense in real life.

Can I use this method for rectangles too?

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No, this only works for squares where all sides are equal. For rectangles, you need both length and width since Area = length × width.

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