Let a, b, and c be three integers, and let a be a perfect...

LUANDATO wrote:Let a, b, and c be three integers, and let a be a perfect square. If a/b = b/c, then which one of the following statements must be true?

(A) c must be an even number
(B) c must be an odd number
(C) c must be a perfect square
(D) c must not be a perfect square
(E) c must be a prime number

The OA is C.

Can any expert help me with this PS question please? I can't understand it. Thanks.

We have a/b = b/c;

Thus, ac = b^2

=> √(ac) = b

√a*√c = Integer

Integer*√c --> Integer; we are given that a is a perfect square, thus √a = integer

Since the product of an integer and √c is an integer, it implies that √c is an integer or c is a perfect square integer.

The correct answer: C

Hope this helps!

-Jay

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