The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse \( c \) is equal to the sum of the squares of the lengths of the other two sides \( a \) and \( b \):
\[ c^2 = a^2 + b^2 \]
For a square with side length \( s \), both \( a \) and \( b \) are equal to \( s \). Thus, the diagonal \( d \) of the square can be calculated as follows:
\[ d^2 = s^2 + s^2 = 2s^2 \]
Taking the square root of both sides gives us:
\[ d = \sqrt{2s^2} = s\sqrt{2} \]
If we take \( s = 4 \) (assuming this is the side length of the square from the options provided), the diagonal would be:
\[ d = 4\sqrt{2} \approx 4 \times 1.4142 = 5.6568 \]
Now, rounding to the nearest hundredth:
\[ d \approx 5.66 \]
However, if we are simply responding based on the given options without a specific side length provided, we look at the anticipated results: 8, 4, 4.24, 2.83.
If you are looking for a general answer, the closest option to the actual diagonal calculations for a square is not present. If \( s = 4 \), then these specific results lead to:
- No correct answer in the original options, since 5.66 isn’t listed.
However, confirming with the smallest side length of 2 (which gives \( d \approx 2.83 \)) fits among the options. Thus:
If negligible information about side length isn’t available, the closest value representing a diagonal calculation we find plausible is:
\[ \boxed{2.83} \]
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