anonymous
  • anonymous
Find the smallest positive integer 'k' such that 360k is a cube number. Can somebody please explain how to do this?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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hartnn
  • hartnn
a cube number is of the form, x*x*x can you factorize 360 ?
anonymous
  • anonymous
36*10 = 2*2*3*3*2*5 and you'll need 3 of each...
anonymous
  • anonymous
360k = (180)(2)k = (90)(2)(2)k = (45)(2)(2)(2)k = (15)(3)(2)(2)(2)k = (5)(3)(3)(2)(2)(2)k and now you can see what do you need to have a perfect cube: if you have \[(5)^{1} (3)^{2} (2)^{3} (k)\] ... then?

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anonymous
  • anonymous
Thank you
anonymous
  • anonymous
did you find k? if so, share please
anonymous
  • anonymous
not quite... 360 = 2*2*2*3*3*5 so you need to multiply by 3*5*5 = k in order to make the smallest perfect cube. make sense? you need 3 of each and you already have three 2's but only two 3's and one 5.

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