What is the smallest positive integer nn such that √6,480∗n is a perfect cube? Options
A) 5	B) 5^2	C) 30	D) 30^2	E) 30^4
Sol: Let's factorize 6480 and we get 6480= 3^4*2^4*5   Now we need to see for what minimum value of n√n*6480= a^3 where a is an Integer   So from 6480 we already have 2^4*3^4*5*n√n = (2^2)^3* (3^2)^3*(5)^3 why cause a is an integer which will need to be have the same factors which are in LHS   solving for n√n = (2^6*3^6*5^3)/ 2^4*3^4*5 and we get   n√n= 2^2*3^2*5^2   Or n = 2^4*3^4*5^4 or 30^4   Answer is 30^4
<result>E</result>
What is the smallest positive integer nn such that √6,480∗n is a perfect cube?