What is the smallest number you can multiply 200 by to make a cube number?

2 Answers
Apr 10, 2017

#200*5# is #1000#, which is #10^3#

May 10, 2017

#5#

Explanation:

firstly let us split 200 into prime factors

#200=100xx2#

#200=50xx2xx2#

#200=25xx2xx2xx2#

#200=5xx5xx2xx2xx2#

#200=5^2xx2^3#

for a cubed number all the powers must be multiples of #3#

The power of #2# is #3# which is a multiple of #3#

The power of #5# is #2# which is not. We need another #5# to make #5^3#

so the smallest number to multiply 200 by to get a cube number is #5#