If x is a positive integer, which of the following CANNOT be expressed as n 2 , where n is an integer?
x^ 5
x ^2 −1
√x ^8
x^2 +1
√ x 5
x^ 5
x ^2 −1
√x ^8
x^2 +1
√ x 5
n² is a PERFECT SQUARE.If x is a positive integer, which of the following CANNOT be expressed as n², where n is an integer?
A) x�
B) x² - 1
C) √x�
D) x² + 1
E) √x�
Question stem, rephrased:
Which of the following is NOT a perfect square?
Perfect squares are 0, 1, 4, 9, 16, 25...
Test the SMALLEST POSSIBLE CASE.
Test x=1 in the answer choices.
Eliminate any answer choice that becomes a perfect square when x=1.
A) x� = 1� = 1.
B) x² - 1 = 1² - 1 = 1 -1 = 0.
C) √x� = √1� = √1 = 1.
D) x² + 1 = 1² + 1 = 1 + 1 = 2.
E) √x� = √1� = √1 = 1.
Eliminate the options in red.
The correct answer is D.
