The shaded region above includes which of the following integers?

Rationale

81 is the integer included in the shaded region above.

The shaded region in the question represents numbers that are perfect squares, and among the options provided, 81 is the only perfect square as it is \(9^2\).

A (16) YOUR ANSWER

16 is a perfect square, as it equals \(4^2\). However, it is not included in the shaded region based on the graphical representation, which likely encompasses numbers larger than 16.

B (27) YOUR ANSWER

27 is not a perfect square; it falls between \(5^2\) (25) and \(6^2\) (36) but does not equal the square of any integer. Therefore, it cannot be part of the shaded region defined by perfect squares.

C (36) YOUR ANSWER

36 is a perfect square since it equals \(6^2\). Similar to 16, while it is a perfect square, it does not appear in the shaded region, which seems to include only larger perfect squares.

D (49) YOUR ANSWER

49 is a perfect square as it equals \(7^2\). However, like 16 and 36, it does not fall within the specified shaded region that includes only larger perfect squares.

E (81) CORRECT

81 is indeed a perfect square since it equals \(9^2\), and it is the only integer among the options that fits within the shaded region's criteria.

Conclusion

The shaded region above is defined by the inclusion of perfect squares. Out of the provided options, 81 stands out as the only integer fitting this description, confirming its presence in the shaded area. The other choices, while some are perfect squares, do not meet the criteria set by the shaded region's scope.

The shaded region above includes which of the following integers?

81 is the integer included in the shaded region above.

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