The product of two numbers is the resulting number when they are multiplied together.
As there is an infinite amount of numbers it would be impossible to write out the result of the product of all pairs of numbers
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An ordered pair is a pair of numbers, in cases where the order is relevant. Often used to indicate coordinates. Also, in general, to create new (larger) sets out of existing sets, in a process known as "Cartesian product"
Ordered pair (s)
A reciprocal (not reciprical) or multiplicative-inverse is THE relationship between two expressions factored from unity. The product of a reciprocal pair of expressions (quantities or numbers) is equal to 1. For example; 1/5 and 5 are reciprocals of each other, they multiply to equal 1. Zero (zed) does not have a reciprocal.
The two numbers that have a product of 30 and a sum of 9 are 3 and 10. This is because 3 multiplied by 10 equals 30, and 3 plus 10 equals 13. Since the sum of the numbers is 9, we can deduce that 3 and 10 are the correct pair of numbers that satisfy both conditions simultaneously.
No. The product of sqrt(2) and sqrt(2) is 2, a rational number. Consider surds of the form a+sqrt(b) where a and b are rational but sqrt(b) is irrational. The surd has a conjugate pair which is a - sqrt(b). Both these are irrational, but their product is a2 - b, which is rational.