If y is the smallest positive integer such that 3,150 multiplied by y is the square of an integer, then y must be :
A. 2
B. 5
C. 6
D. 7
E. 14
A. 2
B. 5
C. 6
D. 7
E. 14
I think it is E - 14. If you break 3150 into it's prime factors, you get
3150 = 2*3*3*5*5*7 = (3^2) * (5^2) * 2 * 7 = (15^2)*2*7
For 3150 to be expressed as a square of an integer, the 2 and 7 in the prime factorization need to be multiplied by another 2 and another 7, which would give us
3150 * y = 3150*14 = (3^2)*(5^2)*(2^2)*(7^2) = 210^2,
so y=14.
