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SteveThe first 10 perfect square numbers are the squares of the first ten natural (or counting) numbers:
1² = 1
2² = 4
3² = 9
4² = 16
5² = 25
6² = 36
7² = 49
8² = 64
9² = 81
10² = 100
Although 0² = 0, zero can also be obtained by any number (not just 0) times zero, eg 2 × 0 = 0, so I've not included it in the list.
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Is 10 a perfect square?
no, 10 is not a perfect square. in order for a number to be a perfect square, you have to see if the numbers that are multiplied to get it are the same. for example: 2x2=4; 4 is a perfect square. 12x12=144; 144 is also a perfect square 5x2=10 or 10x1=10. 10 isn't a perfect square because 5 and 2, and 10 and 1, are different numbers.
How many numbers from 10 through 100 have the sum of their digits equal to a perfect square?
18
How many numbers from 10 through 95 have the sum of their digits equal to a perfect square?
16 of them.
How many numbers 10 through 87 have the sum of their digits equal to a perfect square?
To find the numbers between 10 and 87 with the sum of their digits equal to a perfect square, we need to consider each number individually. The perfect squares between 1 and 9 are 1, 4, and 9. For each perfect square, we can list the numbers that meet the criteria: For the perfect square 1, the numbers are 10, 19, 28, 37, 46, 55, 64, 73, 82. For the perfect square 4, the numbers are 40, 49, 58, 67, 76, 85. For the perfect square 9, the numbers are 90. Therefore, there are 14 numbers between 10 and 87 that have the sum of their digits equal to a perfect square.
How many perfect square numbers are between 2000 and 3000?
√2000 ≅ 44.7 √3000 ≅ 54.8 The squares of 45 to 54 lie within the range 2000 to 3000. There are thus 10 perfect square numbers between 2000 and 3000.
