5 numbers:
53 = 125
63 = 216
73 = 343
83 = 512
93 = 729
There are a total of 5 positive three-digit perfect cubes that are even. To find this, we first determine the range of three-digit perfect cubes, which is from 46 to 96. Then, we identify the even perfect cubes within this range, which are 64, 216, 512, 729, and 1000.
100
The answer will depend on how many digits there are in each of the 30 numbers. If the 30 numbers are all 6-digit numbers then the answer is NONE! If the 30 numbers are the first 30 counting numbers then there are 126 combinations of five 1-digit numbers, 1764 combinations of three 1-digit numbers and one 2-digit number, and 1710 combinations of one 1-digit number and two 2-digit numbers. That makes a total of 3600 5-digit combinations.
Between the two numbers there are only two.
There are 84 such numbers.
There are a total of 5 positive three-digit perfect cubes that are even. To find this, we first determine the range of three-digit perfect cubes, which is from 46 to 96. Then, we identify the even perfect cubes within this range, which are 64, 216, 512, 729, and 1000.
The perfect cubes among the first 1000 natural numbers are the cubes of the integers from 1 to 10, since (10^3 = 1000). These integers are 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. Therefore, there are 10 perfect cubes in the first 1000 natural numbers.
none
25
The cube root of 5000 is approx 17.1 So the numbers 1 to 17 have cubes which are smaller than 5000 that is, there are 17 such numbers.
102 = 100 which is the first possible three digit number that is a perfect square. 312 = 961 which is the last possible three digit number that is a perfect square. So there are 22 three digit positive numbers that are perfect squares.
To find how many two-digit numbers have digits whose sum is a perfect square, we first note that the two-digit numbers range from 10 to 99. The possible sums of the digits (tens digit (a) and units digit (b)) can range from 1 (1+0) to 18 (9+9). The perfect squares within this range are 1, 4, 9, and 16. Analyzing each case, we find the valid combinations for each perfect square, leading to a total of 36 two-digit numbers whose digits sum to a perfect square.
69
13 cubes 4,9,16,25,36,46,64,81,100,121,144,169,196
Total number of 2-digit numbers = (99 - 9) = 90 of themEvery number that isn't a perfect square has an even number of factors.2-digit numbers that are perfect squares: 16, 25, 36, 49, 64, and 81 = 6 of themRemaining 2-digit numbers = (99 - 6) = 93 .
To find how many numbers from 10 to 93 have the sum of their digits equal to a perfect square, we first identify the possible perfect squares within the range of digit sums. The digit sum of a two-digit number ranges from 1 (for 10) to 18 (for 93). The perfect squares in this range are 1, 4, 9, and 16. By calculating the digit sums for each number from 10 to 93, we can determine that the numbers with digit sums equal to these perfect squares are 10-19 (sum = 1, 4, 9), and some others up to 93, yielding a total of 38 numbers.
There are infinitely many cubes between any two numbers - no matter how close together they are. However, there may be a more useful answer in terms of "perfect" cubes: 43 = 64 < 100 < 53 = 125 and 83 = 512 < 600 < 93 = 729 So there are 4 perfect cubes in the range - those of 5 6, 7 and 8.