A square has a side length measuring 2 the square root of 8 centimeters. What do you know about the square? Question 5Select one: a. Both its area and its perimeter are irrational. b. Both its area and its perimeter are rational. c. Its area is rational and its perimeter is irrational. d. Its area is irrational and its perimeter is rational.

To analyze the square:

1. The side length is given as \( 2\sqrt{8} \) cm.

   We simplify this:
   \[
   2\sqrt{8} = 2\sqrt{4 \times 2} = 2 \times 2\sqrt{2} = 4\sqrt{2} \, \text{cm}
   \]
   So, the side length of the square is \( 4\sqrt{2} \) cm.

2. **Perimeter**: 
   The perimeter of a square is given by \( 4 \times \text{side length} \). Thus:
   \[
   \text{Perimeter} = 4 \times 4\sqrt{2} = 16\sqrt{2} \, \text{cm}
   \]
   Since \( \sqrt{2} \) is irrational, the perimeter is irrational.

3. **Area**: 
   The area of a square is given by \( \text{side length}^2 \). So:
   \[
   \text{Area} = (4\sqrt{2})^2 = 16 \times 2 = 32 \, \text{square cm}
   \]
   The area is \( 32 \), which is a rational number.

### Conclusion:
- The area is rational.
- The perimeter is irrational.

Thus, the correct answer is:

**c. Its area is rational and its perimeter is irrational.**

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Would you like more details on this? Here are 5 related questions:

1. How can you calculate the area of a rectangle if given irrational side lengths?
2. How do you determine if a number is rational or irrational?
3. Can a square have both a rational area and a rational perimeter with an irrational side length?
4. How do you simplify expressions involving square roots like \( 2\sqrt{8} \)?
5. What is the significance of irrational numbers in geometry?

**Tip:** Always simplify square roots when possible to avoid calculation errors!

A square has a side length measuring 2 the square root of 8 centimeters. What do you know about the square? Select one: a. Both its area and its perimeter are irrational. b. Both its area and its perimeter are rational. c. Its area is rational and its perimeter is irrational. d. Its area is irrational and its perimeter is rational.

Learn how to determine the perimeter and area of a square with a side length of 2√8 cm. This detailed explanation covers key concepts in geometry, including simplifying square roots and identifying rational and irrational values. Suitable for students in Grades 6-8.

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