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 a×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 × √2 = 2
It is clear that 2 is not an irrational number.
Hence, irrational numbers are not closed under multiplication.
