For how many integers with is an integer?
Answer and explanation
Correct answer: D.
- Step 1: Factor . For the square root to be an integer, must be a perfect square, requiring for positive integer .
- Step 2: Set up the inequality .
- Step 3: The allowable integer values for are (). Thus, there are such integers.
Answer
.
Why not the others: counts only even values of ; counts squares up to ; computes ; is an off-by-one undercount.
Practise more Powers and roots.
Free questions with an explanation for every one, and full timed GRE mock tests.