What is the smallest number i must multiply 315 in order to make it a perfect cube?

Question

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.

Answer 1

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.

Answer 2

Snallest number meaning what is the number you can multiply 315 so that it becomes a perfect cube.

Answer 3

then 1/315 is the smallest number you can multiply 315 by to make a perfect cube.

Answer 4

And what's the next number after that? It needs to be a whole number.

Answer 5

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..

Answer 6

Ok thank you so much! Now it makes sense

Answer 7

what is the smallest number that i must multiply 315 to get a perfect cube