Square S has area 2√2 square units. What is the length of a side of square S?

Rationale

The length of a side of square S is √8 units.

To find the side length of a square given its area, we take the square root of the area. Since the area of square S is 2√2 square units, the side length is √(2√2), which simplifies to √8.

A (√128) YOUR ANSWER

The length √128 simplifies to √(64 * 2) = 8√2, which is much larger than the correct side length. This value would correspond to an area of 128 square units, not the given area of 2√2 square units.

B (√32) YOUR ANSWER

The length √32 simplifies to √(16 * 2) = 4√2. This value would yield an area of 32 square units, significantly exceeding the area of square S, which is only 2√2 square units.

C (√8) CORRECT

The length √8 simplifies to 2√2, which when squared gives an area of (2√2)² = 8 square units. However, since the area of square S is 2√2, we find that √(2√2) = √8, confirming that the side length is indeed √8 units.

D (√2) YOUR ANSWER

The length √2 corresponds to an area of (√2)² = 2 square units. This area is still larger than the area of square S, which is 2√2 square units, making this choice incorrect.

Conclusion

The side length of square S is derived from its area by taking the square root, leading us to the value of √8. Other options either exceed or do not match the specified area of 2√2 square units, reinforcing that √8 is the only correct answer. This process illustrates how understanding the relationship between area and side length is crucial in geometry.

Square S has area 2√2 square units. What is the length of a side of square S?

The length of a side of square S is √8 units.

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