Are the irrational numbers closed under multiplication?

Accepted Solution

Answer:No, irrational numbers are not closed under multiplication.Step-by-step explanation:Irrational numbers are the numbers that cannot be demonstrated in the form of a fraction [tex]\frac{x}{y}[/tex]. We can define rational numbers in other ways as well. Irrational numbers are the numbers which when written in decimal form, the decimal expansion does not end. For example √2, √3, etc.The closed property of multiplication of irrational numbers state that if two irrational numbers are multiplied, then their product is also an irrational number.Let a and b be two irrational numbers, then aΓ—b = c(c is product of a and b), c should also be an irrational number.Irrational numbers are not closed under multiplication and this can be illustrated with the help of an example:√2 Γ— √2 = 2It is clear that 2 is not an irrational number.Hence, irrational numbers are not closed under multiplication.