Multiple-choice question …

E) 0 is correct.

We must compare the given expression with square expressions.

Observe that c2 + 5c + 6 = (c + 2)(c + 3), and, since c is a positive

whole number,

(c + 2)

2

< (c + 2)(c + 3) < (c + 3)

2.

This places it between two consecutive squares, hence c2+5c+6 can never

be a perfect square. There is no number of required form between 1 and

100: (D) is correct.

We must compare the given expression with square expressions.

Observe that , and, since is a positive whole number,

This places it between two consecutive squares, hence can never be a perfect square. There is no number of required form between 1 and 100.

(Problem & solution from: a primer for mathematics competitions)

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