What is the smallest number i must multiply 315 in order to make it a perfect cube?
Please tell me the method you sed and how you got the answer. I've been doing guess and check and it is time consuming.
list of perfect cubes
1, 8, 27, 64, 125, 216, 343, 512, 729, 1,000, 1,331, 1,728, 2,197, 2,744, 3,375...
Smallest number? multiply it by 1/315 and you get the perfect cube 1.
Now I am not sure if your teacher really wanted the "smallest Number" that you should use as a multiplier. Sometimes folks don't think when they ask questions.
Snallest number meaning what is the number you can multiply 315 so that it becomes a perfect cube.
then 1/315 is the smallest number you can multiply 315 by to make a perfect cube.
And what's the next number after that? It needs to be a whole number.
Then the question should be "what is the smallest "whole number" that can be multiplied by 315 to make a perfect cube.
(315*n) = perfect cube
n=perfectcube/315
So for n to be a whole number, the perfect cube must end in 5 or zero just to satisfy the 5 rule. Now if the perfect cube ends in five or zero, the cube root must end in 5 or zero.
You can test 15^3 in the list above I gave you, it doesn't work, so next is 20^3, 25^3,30^3,35^3...
I used my calculator, and found the first one at 105^3/315=3675
so 315*3675 is a perfect cube..