The problem asks to find the side length of a square, given its area $A$.

The formula for the area of a square is:

$A = s^2$

Where:

• $A$ is the area of the square,
• $s$ is the side length of the square.

To find the side length, we take the square root of the area:

$s = \sqrt{A}$

Now, let's solve for each given area:

a) $A = 50 \, \text{cm}^2$:

$s = \sqrt{50} \approx 7.07 \, \text{cm}$

b) $A = 8 \, \text{mm}^2$:

$s = \sqrt{8} \approx 2.83 \, \text{mm}$

c) $A = 169 \, \text{cm}^2$:

$s = \sqrt{169} = 13 \, \text{cm}$

Would you like more details or clarifications on any part of this?

Here are 5 related questions to expand on this concept:

1. How does the area of a square change if the side length is doubled?
2. If the area is given in meters squared, how does that affect the side length calculation?
3. What would the side length be if the area of the square is $25 \, \text{m}^2$?
4. How would you find the perimeter of the square once you know the side length?
5. What is the relationship between the side length and the diagonal of a square?

Tip: When calculating square roots, try to estimate first, especially when the area is not a perfect square, to gauge your answer.