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What is the least positive integer k for which 15k is the cube of a number?
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What is the least positive integer x for which 12x is the cube of an integer?
2
What is the least positive integer n such that the product 800n is a perfect cube?
10
What is the difference between a cube and a perfect cube?
A cube is any number multiplied by itself three times, eg 2 cubed = 2³ = 2×2×2 = 8; 1.5³ = 1.5×1.5×1.5 = 3.375 A perfect cube is an integer (whole number) that is the cube of an integer, eg 8 is a perfect cube as it is 2 cubed, but 9 is not a perfect cube as 9 = 2.08008382...³
Is the cube root of a negative number positive or negative?
The cube root of a negative number is negative
Can the cube root of a positive number ever be a negative number?
No.
What is the least positive integer x for which 12x is the cube of an integer?
2
What is the least positive integer x for which 594x is the cube of an integer?
x = 484
What is the least positive integer n such that the product 800n is a perfect cube?
10
What is the least positive integer a for which 25a is the cube integer?
The only solution is that a = 5 then 25a = 25 x 5 = 52 x 5 = 53.
What is the smallest positive integer e such that the cube root of 600e is an integer?
45
What is the difference between a cube and a perfect cube?
A cube is any number multiplied by itself three times, eg 2 cubed = 2³ = 2×2×2 = 8; 1.5³ = 1.5×1.5×1.5 = 3.375 A perfect cube is an integer (whole number) that is the cube of an integer, eg 8 is a perfect cube as it is 2 cubed, but 9 is not a perfect cube as 9 = 2.08008382...³
Is 77 a cube number?
If by cube you mean perfect cube (a cube of an integer), then no, and the nearest perfect cube is 81.
Explain with workings What is the smallest positive integer q such that 25q is a perfect cube?
5
What is the integer zero of itself?
It is the additive inverse of itself, it is the square, cube, ... any positive power of itself.
Is the cube root of a negative number positive or negative?
The cube root of a negative number is negative
Can the cube root of a positive number ever be a negative number?
No.
How do you find the smallest positive integer of a variable in a cube root so that the cube root is an integer ex. find the smallest positive integer g so that the cube root of 400g is an integer?
Here is a method: cube root of 400g = n, where n is an integer cube both sides: 400g = n3 then: g = n3/400 therefore: n3/400 must be an integer if this is so, then n3 must be divisible by 400 with no remainder, and n must be => cube root of 400 which is 7.368 bracket the answer by substitution: let n=8, n cubed = 512 no good let n=12, n cubed = 1728 no good let n=20, n cubed = 8000, 8000/400=20 OK No smaller value of n will be divisible by 400 without a remainder, so g=20 is the smallest positive integer that meets the requirement.
