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The proposition in the question is simply not true so there can be no answer!
For example, if given the integer 6:
there are no two perfect squares whose sum is 6,
there are no two perfect squares whose difference is 6,
there are no two perfect squares whose product is 6,
there are no two perfect squares whose quotient is 6.
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Can 8081 be the sum of two perfect squares?
8081 can be the sum of two perfect squares because its perfect squares are 41 x41+80x80=1681+6400. Answer=1681+6400
Counter example that a positive integer is not equal to the sum of two squares?
3 is the smallest integer that cannot be written as the sum of two squares. This is easy to see, since the only squares less than or equal to 3 are 0 and 1.
What you have learn in product of perfect square?
That the set of perfect squares is closed under multiplication. That is if x and y are any two perfect squares, then x*y is a perfect square.
What two square numbers total 21?
There is no pair of perfect squares that sums to 21. And the question is pointless if it is not about perfect squares because in that case there are infinitely many answers.There is no pair of perfect squares that sums to 21. And the question is pointless if it is not about perfect squares because in that case there are infinitely many answers.There is no pair of perfect squares that sums to 21. And the question is pointless if it is not about perfect squares because in that case there are infinitely many answers.There is no pair of perfect squares that sums to 21. And the question is pointless if it is not about perfect squares because in that case there are infinitely many answers.
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
Is the product of two perfect squares sometimes a perfect square?
yes..always a perfect square A perfect square is the product of an integer by itself. If you multiply a perfect square x² by another perfect square y² you get x²y² = x·x·y·y = x·y·x·y = (x·y)² which is a perfect square. Note that the product of two integers will also be an integer so x·y must be an integer because if x² and y² are perfect squares x must be an integer and y must be an integer and x·y is therefore a product of 2 integers.
Why are all the perfect squares are rational number?
A perfect square is a square of an integer.The set of integers is closed under multiplication. That means that the product of any two integer is an integer. Therefore the square of an integer is an integer.Integers are rational numbers so the square [which is an integer] is a rational number.
Can 8081 be the sum of two perfect squares?
8081 can be the sum of two perfect squares because its perfect squares are 41 x41+80x80=1681+6400. Answer=1681+6400
How many numbers between 30 and 50 are perfect squares?
Two. 36, and 49 are perfect squares.
What is the difference of 2 perfect squares?
This is when two perfect squares(ex.) [x squared minus 4] a question in which there are two perfect squares. you would find the square root of each. then it depends on what kind of math your doing.
Counter example that a positive integer is not equal to the sum of two squares?
3 is the smallest integer that cannot be written as the sum of two squares. This is easy to see, since the only squares less than or equal to 3 are 0 and 1.
What you have learn in product of perfect square?
That the set of perfect squares is closed under multiplication. That is if x and y are any two perfect squares, then x*y is a perfect square.
What two square numbers total 21?
There is no pair of perfect squares that sums to 21. And the question is pointless if it is not about perfect squares because in that case there are infinitely many answers.There is no pair of perfect squares that sums to 21. And the question is pointless if it is not about perfect squares because in that case there are infinitely many answers.There is no pair of perfect squares that sums to 21. And the question is pointless if it is not about perfect squares because in that case there are infinitely many answers.There is no pair of perfect squares that sums to 21. And the question is pointless if it is not about perfect squares because in that case there are infinitely many answers.
What is the probability that a randomly selected two-digit positive integer is a perfect square or a perfect cube?
There are 90 two-digit numbers from 10 to 99. Of those, 6 are perfect squares (16, 25, 36, 49, 64, and 81) and 2 are perfect cubes (27 and 64). Each perfect square or root has a probability of 1 in 90 in being drawn.
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 is two perfect squares that equal 29?
4 and 25.
What are two perfect squares that have the sum of 100?
64 and 36.
