If 175*s is a perfect square then s can be which of the following numbers? Select.
A) 21 B) 35 C) 54 D) 105 E) 150
My solution:   For a number to be a perfect square all the prime factors must be in pairs. So,   Prime factors of 175 are 5 *5 * 7   1) 21 = 3 * 7   2) 35 = 5 * 7   3) 54 = 2 * 3 * 3 * 3   4) 105 = 3 * 5 * 7   5) 150 = 2 * 3 * 5 * 5   So only answer choice D completes the pairing of 5 and 7. It adds a3, a5, and a7to the prime factors of 175 (5*5*7) and makes it a perfect square. 35
<result>B</result>
If 175*s is a perfect square then s can be which of the following numbers?