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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.
What else can I help you with?
What is perfect square number?
A perfect square is a number that can be expressed as the product of two equal integers.
Why 8 is not a perfect square?
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.
Is 50 a perfect square explain?
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.
What is the link between the product of any four consecutive positive integers and some square numbers?
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
What two consective integers does the square root of 15 lie?
-4 and -3 is one possible answer. 3 and 4 is the other.
What is perfect square number?
A perfect square is a number that can be expressed as the product of two equal integers.
Is nine fourths a a perfect square?
No, a perfect square is a number that can be expressed as the product of two equal integers.
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 8 is not a perfect square?
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.
What is the perfect square?
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.
Is 50 a perfect square explain?
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.
What is the perfect square number?
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.
What is the link between the product of any four consecutive positive integers and some square numbers?
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
What two consective integers does the square root of 15 lie?
-4 and -3 is one possible answer. 3 and 4 is the other.
Is the product of a perfect square and a perfect square closed under multiplication?
Yes, the product of two perfect squares is also a perfect square. If ( a ) and ( b ) are perfect squares, they can be expressed as ( a = x^2 ) and ( b = y^2 ) for some integers ( x ) and ( y ). Their product ( ab = x^2y^2 = (xy)^2 ), which is a perfect square. Thus, the set of perfect squares is closed under multiplication.
Has integers as its square root?
Such a number is called a "perfect square".
What is a number that has integers as its square roots?
It is a perfect square.
