Explain why multiplying two irrational numbers could result in either an irrational number or a rational number.
Multiplying two irrational numbers can result in either an irrational number or a rational number because the properties of irrational numbers are not preserved under multiplication.
In some cases, when multiplying two irrational numbers, the result may be a rational number. For example, multiplying the irrational numbers √2 and √2 results in 2, which is a rational number. This is because the product of these two irrational numbers happens to be a perfect square, which can always be written as a rational number.
On the other hand, there are also cases where multiplying two irrational numbers results in an irrational number. For example, multiplying the irrational numbers √2 and √3 results in the irrational number √6. This is because the product of these two irrational numbers does not simplify to a rational number.
Therefore, multiplying two irrational numbers can result in either an irrational number or a rational number depending on the specific numbers being multiplied.