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You can factor 540 into prime factors. Then, for each prime factor that doesn't appear 3, 6, 9, ... times, add additional factors to complete a multiple of 3. These factors will make up the number "k".
Oh, dude, so like, the smallest integer k such that 540k is a cube number is 125. Because, you know, 540 times 125 equals 67500, which is a cube number. It's like math magic, but with cubes instead of rabbits.
To find the smallest integer k such that 540k is a cube number, we need to factorize 540 into its prime factors: 2^2 * 3^3 * 5. To make 540k a cube number, we need to balance the powers of each prime factor such that they are all multiples of 3. Therefore, we need to find the smallest integer k such that the powers of 2, 3, and 5 in 540k are all multiples of 3. This means k = 3^2 * 5^2 = 225.
Oh, what a happy little math problem! To find the smallest integer k such that 540k is a cube number, we need to break down 540 into its prime factors: 2^2 * 3^3 * 5. To make 540k a cube number, we need to balance the powers of each prime factor, so k must be 2 * 3^2 * 5^2 = 450. So, the smallest integer k that makes 540k a cube number is 450.
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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.
What is the smallest integer greater than 1 that is both a perfect square and perfect cube?
its 81
The cube root of this number is one more than the smallest prime?
The cube root of this number is one more than the smallest prime
Which is the smallest natural number ending in '5' that is a perfect cube?
125
What is a perfect cube number?
A perfect cube is the cube of an integer (whole number). This means that, for n to be a perfect cube, n = x3, x∈ℤ Eg. ±1 [=(±1)3], 8 [=(±2)3], ±27 [= (±3)3], etc.
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
What is the smallest positive integer e such that the cube root of 600e is an integer?
45
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.
Explain with workings What is the smallest positive integer q such that 25q is a perfect cube?
5
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.
What is the smallest integer greater than 1 that is both a perfect square and perfect cube?
its 81
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
What is the smallest number that is a cube and a square number?
4
The cube root of this number is 1 more than the smallest prime?
The cube root of this number is 1 more than the smallest prime?
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.
The cube root of this number is one more than the smallest prime?
The cube root of this number is one more than the smallest prime
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.
