Calculate Side Length: Finding Square Root of Area 16

Square Root Applications with Perfect Squares

How long are the sides of a square that has an area of 16?

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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)
00:10 Substitute appropriate values and solve to find the side
00:18 Take the square root
00:24 When taking a square root there are always 2 solutions
00:28 The side length must be greater than 0
00:32 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

How long are the sides of a square that has an area of 16?

2

Step-by-step solution

We need to determine the side length of a square whose area is 16.

  • Step 1: Set up the equation using the area formula for a square, A=s2 A = s^2 . Given the area A=16 A = 16 , we have:
    s2=16 s^2 = 16
  • Step 2: Solve for s s by taking the square root of both sides:
    s=16 s = \sqrt{16}
  • Step 3: Calculate the square root:
    s=4 s = 4

Since a side length cannot be negative, we take only the positive square root. Therefore, the side length of the square is 4 4 , which corresponds to choice 4.

3

Final Answer

4

Key Points to Remember

Essential concepts to master this topic
  • Formula: Area of square equals side length squared: A=s2 A = s^2
  • Technique: Take square root of area: s=16=4 s = \sqrt{16} = 4
  • Check: Verify by squaring answer: 42=16 4^2 = 16 matches given area ✓

Common Mistakes

Avoid these frequent errors
  • Taking negative square root or forgetting it exists
    Don't think 16=−4 \sqrt{16} = -4 or ignore the negative solution = impossible side length! Side lengths must be positive distances in geometry problems. Always take only the positive square root for measurements.

Practice Quiz

Test your knowledge with interactive questions

\( \sqrt{100}= \)

FAQ

Everything you need to know about this question

Why can't the side length be negative 4?

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Great question! While (−4)2=16 (-4)^2 = 16 mathematically, side lengths represent physical distances which are always positive. In geometry, we only use positive values for measurements.

How do I know 16 is a perfect square?

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Perfect squares are numbers like 1, 4, 9, 16, 25... that result from squaring whole numbers. Since 42=16 4^2 = 16 , we know 16 is a perfect square with exact square root 4.

What if the area wasn't a perfect square?

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You'd still take the square root, but it might be a decimal or irrational number. For example, if area = 15, then s=15≈3.87 s = \sqrt{15} \approx 3.87 .

Do I always use the area formula for squares?

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Yes! For any square problem involving area and side length, always start with A=s2 A = s^2 . This formula connects the two measurements directly.

How can I remember which operation to use?

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Think: "Area to side = square root, side to area = square." Going from area (16) to side length means taking 16 \sqrt{16} !

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