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Bunuel
mrwaxy
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
Detailed explanation would be appreciated.
\(3,150=2*3^2*5^2*7\), now \(3,150*y\) to be a perfect square \(y\) must complete the odd powers of 2 and 7 to even number (perfect square has even powers of its primes), so the least value of \(y\) is 2*7=14. In this case \(3,150y=(2*3^2*5^2*7)*(2*7)=(2*3*5*7)^2=perfect \ square\).
Prime factoring 3150 = 2 * 3^2 * 5^2 * 7 k = 3150 * y k = 2 * 3^2 * 5^2 * 7 * y k = 14 * 15^2 * y To make k a perfect square, y has to be atleast 14 [ltr][/ltr]
mrwaxy
If y is the smallest positive integer such that 3,150 multiplied by y is the square of an integer, then y must be