Question

Find the smallest value of n so that 180n is a cube number
(show working out please)

Answer 1

n = 1200

180*1200 = 60^3

Answer 2

how did you get that? In a test i'll need to show my working and ill appreciate it if you told me how please

Answer 3

first write 180 as the product of its prime factors:\[180=2^2\times3^2\times5\]to make it into a perfect cube you need to make sure that each of its prime factors is raised to a power that is a multiple of 3.
so we see that it needs to be multiplied by \(2\times3\times5^2=150\) to get:\[180\times150=27000=30^3\]