Give an example to show that the set of irrational numbers is not closed under the operation of multiplication.

Answers

An example to show that the set of irrational numbers is not closed under the operation of multiplication is shown below.

What are irrational numbers?

Irrational numbers are all real numbers that are not rational numbers in mathematics.

Irrational numbers, in other words, cannot be stated as the ratio of two integers.

When the length ratio of two line segments is an irrational number, the line segments are said to be incommensurable, which means that they share no “measure” in common, that is, there is no length, no matter how short, that could be used to express the lengths of both of the given segments as integer multiples of itself.

An example to show that the set of irrational numbers is not closed under the operation of multiplication:

Example: √2 is irrational

√2 × √2 = 2

2 is a rational number.

Therefore, an example to show that the set of irrational numbers is not closed under the operation of multiplication is shown.

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