A perfect cube is an integer whose cube root is an integer. For example, 27, 64 and 125 are perfect cubes. If p and q are perfect cubes, which of the following will not necessarily be a perfect cube?	Choose the correct choice:
A) 8p
B) pq
C) pq + 27
D) -p
E) (p - q)^6
A. since p is a perfect cube and 8 is a perfect cube, 8p will be a perfect cube. reject.   B. since p is a perfect cube and q is a perfect cube, pq will be a perfect cube. reject.   C. Hold.   D. since p is a perfect cube, -p will also be a perfect cube. reject.   E. (p-q)^6, is a perfect cube, so reject.   By elimination C is the answer.   Check say p = 1, q=8, then 8+27= 
<gadget id="calculator">8+27</gadget>
<output>35</output>
35 --&gt; not a perfect cube.   ANSWER:pq + 27
<result>C</result>
A perfect cube is an integer whose cube root is an integer. For example, 27, 64 and 125 are perfect cubes. If p and q are perfect cubes, which of the following will not necessarily be a perfect cube?