0
What else can I help you with?
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 multiple of 56 which is a perfect cube?
2744
What is interesting about Hardy-Ramanujan number?
1729 is the smallest number that can be expressed in two ways as the sum of two cubes.[12cube+9cube] * * * * * ... two positive cubes. 12 cube + 1 cube and 10 cube + 9 cube.
How many positive integers have equally many digits in the decimal representation of their square and their cube?
3
Can a prime number be a perfect cube?
Sure, honey, let me break it down for you. No, a prime number cannot be a perfect cube because a prime number is only divisible by 1 and itself. And let me tell you, a perfect cube is the result of multiplying a number by itself three times, so a prime number ain't gonna fit that bill. So, in short, a prime number and a perfect cube are like oil and water - they just don't mix, darling.
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 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
Explain with workings What is the smallest positive integer q such that 25q is a perfect cube?
5
What is the least positive integer k for which 15k is the cube of a number?
To find the least positive integer ( k ) for which ( 15k ) is a cube, we start with the prime factorization of 15, which is ( 3^1 \times 5^1 ). For ( 15k ) to be a perfect cube, the exponents in its prime factorization must be multiples of 3. Thus, we need to make the exponents of both 3 and 5 in ( 15k ) equal to 3. Therefore, ( k ) must contribute ( 3^2 ) (to make the exponent of 3 equal to 3) and ( 5^2 ) (to make the exponent of 5 equal to 3). Thus, ( k = 3^2 \times 5^2 = 9 \times 25 = 225 ). Therefore, the least positive integer ( k ) is ( 225 ).
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
Is 11025 a perfect cube?
No, 11025 is not a perfect cube. A perfect cube is an integer that can be expressed as the cube of another integer. The cube root of 11025 is approximately 22.2, which is not an integer, indicating that 11025 cannot be written as ( n^3 ) for any integer ( n ).
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.
How does finding cube root differ from finding a square root of a positive integer?
Finding the square root of a positive integer involves identifying a number that, when multiplied by itself, equals the original integer, resulting in one non-negative solution. In contrast, finding the cube root of a positive integer determines a number that, when multiplied by itself twice (i.e., raised to the power of three), equals the original integer, yielding one real solution. The key difference lies in the operations involved: square roots deal with pairs of factors, while cube roots involve triplets. Additionally, cube roots can yield real solutions for negative integers, unlike square roots.
The square root of a perfect square and the cube root of a perfect cube is?
an integer
