MATH SOLVE

4 months ago

Q:
# Are the irrational numbers closed under multiplication?

Accepted Solution

A:

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 β2, β3, 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 aΓb = 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:β2 Γ β2 = 2It is clear that 2 is not an irrational number.Hence, irrational numbers are not closed under multiplication.