Raising a number to the power of 3 is the same as multiplying the base 3 times by itself. Use this fact to determine the possible n-values for which (- n)^3 result in a positive number.
- 8
Practice makes perfect
We are asked to find the greatest integer n such that (- n)^3 is positive and its value has a 2 in the ones place.
( - n )^3 = + 2Let's start by determining the possible n-values for which (- n)^3 results in a positive number. To do so, we will pay close attention to the signs. Note that if n=0, then (- n)^3=0. Therefore, we will not consider this case.
Therefore, if we want (- n)^3 to be positive, n must be negative. Now, let's calculate the cubes of the negative integers and see which is the first one that has a value of 2 in the ones place.
n
(- n ) ^3
Value of (- n )^3
- 1
(- (- 1) )^3 = 1^3
1
- 2
(- (- 2) )^3 = 2^3
8
- 3
(- (- 3) )^3 = 3^3
27
- 4
(- (- 4) )^3 = 4^3
64
- 5
(- (- 5) )^3= 5^3
125
- 6
(- (- 6) )^3 = 6^3
216
- 7
(- (- 7) )^3 = 7^3
343
- 8
(- (- 8) )^3 = 8^3
51 2
As we can see, cubing - 8 results in the desired value. As our possibilities are all negative integers, it is the greatest integer that we are looking for.
