If #p and q# are positive integers with #pq = 36,# then #p/q# cannot be.... ? A. 1/4 B. 4/9 C. 1 D. 2 E. 9

1 Answer
George C.
Aug 22, 2017

D #2#

Explanation:

Note that #pq=36 = 6^2# is a perfect square, so #p/q = 6^2/q^2# must be a perfect square too.

All options except D are perfect squares:

A #1/4 = (1/2)^2#

B #4/9 = (2/3)^2#

C #1 = 1^2#

E #9 = 3^2#

D #2# is not a perfect square - Its square root is irrational.

Alternatively, we can fairly quickly find:

A #1/4 = 3/12#

B #4/9 = 4/9#

C #1 = 6/6#

E #9 = 18/2#

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