Find a positive integer that is divisible by 18 and whose cube root is a number between 8 and 8.1.
I want to find a number of the form 18n, where n is a positive integer, such that (18n)^(1/3) is between 8 and 8.1. This means that 8 < (18n)^(1/3) < 8.1, or equivalently, 8^3 < 18n < 8.1^3. I can calculate 8^3 = 512 and 8.1^3 = 531.441. I can divide everything by 18 to get 28.444 < n < 29.525. The only integer in this range is n = 29. Therefore, the number I am looking for is 18n = 18 * 29 = 522. 