0
What else can I help you with?
What number is a perfect square and the sum of 2 perfect squares?
25 = 9 + 16 There are many more sets like these. This one has the smallest numbers.
Can 2819 be expressed by the sum of 2 perfect squares?
no
What is the smallest three digit square number that is the sum of two squares?
The smallest three-digit square number is 100, which is (10^2). However, it cannot be expressed as the sum of two squares. The next three-digit square is 121 ((11^2)), which can be expressed as (11^2 = 10^2 + 1^2). Thus, 121 is the smallest three-digit square number that is also the sum of two squares.
Can 4003 be expressed by the sum of 2 perfect squares?
No. The closest integers which can are 4001 (= 40² + 49²) and 4005 (= 6² + 63²).
Can you write every integer as the sum of two nonzero perfect squares?
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
What number is a perfect square and the sum of 2 perfect squares?
25 = 9 + 16 There are many more sets like these. This one has the smallest numbers.
Can 2819 be expressed by the sum of 2 perfect squares?
no
What is the smallest negative perfect square that is divisible by the four smallest prime numbers?
Perfect squares are positive. A smallest negative number doesn't exist. The four smallest prime numbers are 2, 3, 5 and 7. The smallest perfect square would have to be 2^2 x 3^2 x 5^2 x 7^2 or 44,100
How many perfect squares are between 900-1000?
1900
What is the smallest prime number whose sum of its digits forms a number that is a perfect cube?
I think it will be 17. The sum of digits is 8, which is the cube of 2.
Can 4003 be expressed by the sum of 2 perfect squares?
No. The closest integers which can are 4001 (= 40² + 49²) and 4005 (= 6² + 63²).
Can you write every integer as the sum of two nonzero perfect squares?
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
How many 3 digit numbers are perfect squares?
The smallest three-digit number is 100, and the largest is 999. The smallest integer whose square is a three-digit number is 10 (since (10^2 = 100)), and the largest integer is 31 (since (31^2 = 961)). Therefore, the three-digit perfect squares correspond to the integers from 10 to 31, which gives us a total of (31 - 10 + 1 = 22) three-digit perfect squares.
Why is the product of two perfect squares always a perfect square?
The product of two perfect squares is always a perfect square because a perfect square can be expressed as the square of an integer. If we take two perfect squares, say ( a^2 ) and ( b^2 ), their product can be written as ( a^2 \times b^2 = (a \times b)^2 ). Since ( a \times b ) is an integer, ( (a \times b)^2 ) is also a perfect square, confirming that the product of two perfect squares yields another perfect square.
Is 36 perfect?
No, 36 is not a perfect number. A perfect number is defined as a positive integer that is equal to the sum of its proper divisors (excluding itself). For 36, the proper divisors are 1, 2, 3, 4, 6, 9, and 12, which sum to 37, not 36. The smallest perfect number is 6.
If the regression sum of squares is large relative to the error sum of squares is the regression equation useful for making predictions?
If the regression sum of squares is the explained sum of squares. That is, the sum of squares generated by the regression line. Then you would want the regression sum of squares to be as big as possible since, then the regression line would explain the dispersion of the data well. Alternatively, use the R^2 ratio, which is the ratio of the explained sum of squares to the total sum of squares. (which ranges from 0 to 1) and hence a large number (0.9) would be preferred to (0.2).
How many perfect squares are there between 35 and 111?
To find the perfect squares between 35 and 111, we need to determine the perfect squares closest to these numbers. The closest perfect squares are 36 (6^2) and 100 (10^2). The perfect squares between 36 and 100 are 49 (7^2), 64 (8^2), and 81 (9^2). Therefore, there are 4 perfect squares between 35 and 111: 36, 49, 64, and 81.
