To find the two-digit numbers whose digits sum to a perfect square, we first identify the possible sums of the digits, which range from 1 (1+0) to 18 (9+9). The perfect squares in this range are 1, 4, 9, and 16. The valid two-digit combinations for these sums are: for 4 (14, 23, 32, 41, 50), for 9 (18, 27, 36, 45, 54, 63, 72, 81, 90), and for 16 (79). Counting all valid combinations gives us a total of 20 two-digit numbers.
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.
12689 14689 12489
The smallest 3-digit square number is 100, which is the square of 10 (10 x 10). It is the first perfect square that has three digits.
I am pretty sure you can figure this out on your own. Raise different numbers to the square, until you get a 4-digit result. Similary, calculate the cube of different numbers, until you get a 4-digit number. If you want the SAME number to be both a perfect square and a perfect cube, then it must be a power of 6. In that case, just experiment raising different numbers to the sixth power, until you get a 4-digit number.
The least one-digit number that is a perfect square is 0, as (0^2 = 0). However, if we consider only positive one-digit numbers, then the least perfect square is 1, since (1^2 = 1).
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
If the number with the digits reversed can have a leading 0 so that it is a 1-digit number, then 16. Otherwise 13.
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.
12689 14689 12489
none
The smallest 3-digit square number is 100, which is the square of 10 (10 x 10). It is the first perfect square that has three digits.
I am pretty sure you can figure this out on your own. Raise different numbers to the square, until you get a 4-digit result. Similary, calculate the cube of different numbers, until you get a 4-digit number. If you want the SAME number to be both a perfect square and a perfect cube, then it must be a power of 6. In that case, just experiment raising different numbers to the sixth power, until you get a 4-digit number.
The least one-digit number that is a perfect square is 0, as (0^2 = 0). However, if we consider only positive one-digit numbers, then the least perfect square is 1, since (1^2 = 1).
4,624 = 682
The numbers from 1 to 39 include both single-digit and double-digit numbers. There are 9 single-digit numbers (1 to 9) and 30 double-digit numbers (10 to 39). Therefore, the total number of digits is 9 (from single-digit numbers) + 60 (from double-digit numbers, as each has 2 digits) = 69 digits in total.
With 123 digits you can make 123 one-digit numbers.