20. Square S has area 2√2 square units. What is the length of a side of square S?
Answer: C
The length of a side of square S is √8 units.
To find the length of a side of square S, we take the square root of its area. Since the area of square S is 2√2 square units, the length of a side is √(2√2), which simplifies to √8.
A) √128
This option is incorrect because the square root of 128 is not equal to the length of a side of square S. The correct calculation involves the area being 2√2, which does not relate to √128.
B) √32
This option is also incorrect. The square root of 32 simplifies to 4√2, which does not match the dimension derived from the area of 2√2. Therefore, it cannot represent the length of a side of square S.
C) √8
This option is correct. The length of a side of square S is derived from the area by calculating √(2√2), which simplifies to √8. Hence, this accurately represents the side length of the square.
D) √2
This option is incorrect as well. The square root of 2 does not equal the length of a side of square S. The area calculation does not support this value as a possible length.
Conclusion
The correct answer, √8, is derived from the area of square S, which is 2√2. Other options either simplify to values not related to the given area or simply do not equate to the necessary dimensions. Thus, √8 is the only viable length for a side of square S.