Perfect squares are the result of multiplying integers by themselves: 1 x 1 = 1 2 x 2 = 4 3 x 3 = 9 etc. The perfect squares, above, are the numbers to the right of the equal sign, so just continue until you pass the number 500.
You'll need five. 2 x 2 x 5 x 5 x 5 = 500
No.First of all, you can't write negative numbers as sums of perfect squares at all - since all perfect squares are positive.Second, for natural numbers (1, 2, 3...) you may need up to 4 perfect squares: http://en.wikipedia.org/wiki/Lagrange's_four-square_theoremNo.First of all, you can't write negative numbers as sums of perfect squares at all - since all perfect squares are positive.Second, for natural numbers (1, 2, 3...) you may need up to 4 perfect squares: http://en.wikipedia.org/wiki/Lagrange's_four-square_theoremNo.First of all, you can't write negative numbers as sums of perfect squares at all - since all perfect squares are positive.Second, for natural numbers (1, 2, 3...) you may need up to 4 perfect squares: http://en.wikipedia.org/wiki/Lagrange's_four-square_theoremNo.First of all, you can't write negative numbers as sums of perfect squares at all - since all perfect squares are positive.Second, for natural numbers (1, 2, 3...) you may need up to 4 perfect squares: http://en.wikipedia.org/wiki/Lagrange's_four-square_theorem
3
Perfect square roots are the counting numbers {1, 2, 3, ...} The squares of the perfect square roots are the perfect squares, namely 1² = 1, 2² = 4, 3² = 9, etc.
The 3 digit numbers under 500 are 100 through 499.
Perfect squares are the result of multiplying integers by themselves: 1 x 1 = 1 2 x 2 = 4 3 x 3 = 9 etc. The perfect squares, above, are the numbers to the right of the equal sign, so just continue until you pass the number 500.
There are 417 of them and it would take too long to list them all. You could draw up a list of all 500 numbers and then delete each multiple of 6. There are 83 of them.
There are 232 numbers between 1 and 500 that are divisible by 3 or 5.
No.
You'll need five. 2 x 2 x 5 x 5 x 5 = 500
1000 (2)1500 (3)
1500
400 of them.
No, the natural numbers are not closed under division. For example, 2 and 3 are natural numbers, but 2/3 is not.
The sum of the first 500 positive integers is: 1 + 2 + 3 + ... + 498 + 499 + 500 = 125250
To solve this, try to understand what I'm about to do. The first two numbers are 1 and 3 the last two numbers are 1997 and 1999 1 + 1999 = 2000 3 + 1997 = 2000 etc. Therefore, the numbers can be paired in groups of two. If you did this to every number, you would see that there are 500 groups. So, there are 500 groups that sum to 2000 so multiply the two and you will get 1,000,000