What is the smallest positive integer n such that √126n is an integer?

The smallest n =14, because:

126 = 2 * 3^2 * 7 =3^2 x 14. Then if you multiply by another 14, then:3^2 x 14^2 will give you a square.

Sqrt(3^2 x 14^2) =3 x 14 =42