What is the least possible positive integer-value of N such that √18⋅n⋅34 is an integer?
=√18⋅n⋅34 =√3⋅3⋅2⋅n⋅2⋅17 =√3⋅3⋅2⋅2⋅17⋅n =√3⋅3⋅√2⋅2⋅√17⋅n =3⋅2⋅√17⋅n =6√17n
There must be a pair of 17's in the prime factorization of the number under the sqrt.
So 17 must be a factor of n , and the least possible positive integer value of n is 17
=6√17⋅17 =6⋅17 =102_