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What is the smallest positive integer e such that the cube root of 600e is an integer?
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∙ 16y ago
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∙ 16y ago
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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.
What is the cube root of 700 to the nearest integer?
9
What number's cube root is 1 more then the smallest prime?
The number 27 has a cube root of 3, which is 2 (the smallest prime) plus 1.
A cube number between 600 and 800?
The only cube of an integer in the range 600 - 800 is 9 because 9x9x9= 729.
Cube root of number is 1 more smallest prime?
27
Explain with workings What is the smallest positive integer q such that 25q is a perfect cube?
5
What is the smallest integer where the integer before it is a perfect square and the integer after it is a perfect cube?
The integer is 26
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.
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 smallest integer greater than 1 that is both the square and the cube of an integer?
64 = 4 cubed and 8 squared.
What is the least positive integer n such that the product 800n is a perfect cube?
10
What is the smallest integer greater than 1 that is both a perfect square and perfect cube?
its 81
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 integer zero of itself?
It is the additive inverse of itself, it is the square, cube, ... any positive power of itself.
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
The square root of a perfect square and the cube root of a perfect cube is?
an integer
