Question 319260
First, factor 45n into 3*3*5*n. In order for 3*3*5*n to be a perfect cube, each prime factor must come in sets of triples. So we're missing one 3 and two 5 factors which means that n=3*5*5=75



So the answer is n=75 making the final number to be 45*75=3375



Using a calculator, we find that {{{root(3,3375)=15}}}. We could also notice that since 3*3*3*5*5*5=3375, we can just rearrange the terms to get {{{3^3*5^3=(3*5)^3=15^3=3375}}} which would mean that {{{15^3=3375}}} (ie showing that 3375 is a perfect cube)