Question

Let p, q, and s be integers such that $p^2=s{q}^2.$ Then, it follows that

• A. p is an even number
• B. if s divides p, then s is a perfect square.
• C. s divides p.
• D. $q^2$ divides p.

Answer 1

The correct option is B if s divides p, then s is a perfect square.

If s divides p, then s is a perfect square.

Ex. (i) Let p = 10, q = 5
Then, $p^2=100and{q}^2=25$
s = 4, which is a perfect square.

(ii) Let p = 8, q = 4
Then, $p^2=64and{q}^2=16$
s = 4, which is a perfect square.