Suppose the smallest of the integers is n.
Then the product of the four consecutive integers is n*(n+1)*(n+2)*(n+3)
=(n2+3n)(n2+3n+2) = n4+6n3+11n2+6n
So product +1 = n4+6n3+11n2+6n+1 which can be factorised as follows:
n4+3n3+n2 +3n3+9n2+3n + n2+3n+1
=[n2+3n+1]2
Thus, one more that the product of four consecutive integers is a perfect square.
A perfect square is a number that can be expressed as the product of two equal integers.
The number 8 is not a perfect square because it is not classified as the product of two positive integers. The number 8 is classified as a perfect cube, however.
No, it is not. A perfect square is the product of two equal integers; i.e. 9 is a perfect square. It can be expressed as 3*3. There is no number that when multiplied twice equals 50.
The product of four consecutive integers is always one less than a perfect square. The product of four consecutive integers starting with n will be one less than the square of n2 + 3n + 1
-4 and -3 is one possible answer. 3 and 4 is the other.
A perfect square is a number that can be expressed as the product of two equal integers.
No, a perfect square is a number that can be expressed as the product of two equal integers.
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.
The number 8 is not a perfect square because it is not classified as the product of two positive integers. The number 8 is classified as a perfect cube, however.
A perfect square number is a number that can be expressed as the product of two same common integers. For instance, 16 is a perfect square since it is expressed as 4 x 4. 14 is not the perfect square since it can't be expressed as two common integers. The factors of 14 are 2 and 7.
No, it is not. A perfect square is the product of two equal integers; i.e. 9 is a perfect square. It can be expressed as 3*3. There is no number that when multiplied twice equals 50.
The product of four consecutive integers is always one less than a perfect square. The product of four consecutive integers starting with n will be one less than the square of n2 + 3n + 1
A perfect square number is a number that can be expressed as the product of two same common integers. For instance, 16 is a perfect square since it is expressed as 4 x 4. 14 is not the perfect square since it can't be expressed as two common integers. The factors of 14 are 2 and 7.
-4 and -3 is one possible answer. 3 and 4 is the other.
Such a number is called a "perfect square".
It is a perfect square.
a perfect square