If 375y=x2 and x and y are positive integers,
then which of the following must be an integer?
i. y/15
ii. y/30
iii. (y2)/25

a) i only
b) iii only
c) i and ii
d) i and iii
e) i, ii and iii

Option d - I and III.

Step-by-step explanation:

Given : If and x and y are positive integers.

To find : Which of the following must be an integer?

Solution :

As we see all option there is a multiple of y.

So, we factoring the number 375

i.e.

In order for 375y to be a perfect square,

The prime factorization of y must contain at least one 3 and one 5.

or y must be a multiple of 15.

If y is a multiple of 15, then must be an integer.

and must be an integer.

Therefore, I and III will be correct i.e. option d.

37

step-by-step explanation: