What are those numbers whose unti digit of the cube is equal to the Same number
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What are the digits in the unit's place of the cubes of 1,2,3,4,5,6,7,8,9,10? Is it possible to say that a number is not a perfect cube by looking at the digit in unit's place of the given number, just like we did for squares?
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To determine the digits at unit's place of the cubes of given numbers, first we need to find their cubes.
1
3
=1, 2
3
=8, 3
3
=27, 4
3
=64, 5
3
=125, 6
3
=216, 7
3
=343, 8
3
=512, 9
3
=729, 10
3
=1000
The digits at unit's place are 1,8,7,4,5,6,3,2,9,0
Let's arrange them in order, we get 0,1,2,3,4,5,6,7,8,9 as digits at unit's place.
Each digit occurs at the end of some cube. Hence one cannot conclude that some number is not a cube by looking at the last digit