The product of two irrational numbers can be which of the following?

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Multiple Choice

The product of two irrational numbers can be which of the following?

Explanation:
The key idea is that multiplying two irrational numbers doesn’t fix the result to be one type of number. It can end up rational or irrational. For example, sqrt(2) times sqrt(2) equals 2, which is rational. But sqrt(2) times sqrt(3) equals sqrt(6), which is irrational. There are many other cases where the product is rational, like sqrt(8) times sqrt(2) equals 4. Since we can obtain both rational and irrational results, the product of two irrational numbers can be either. It’s not undefined, because multiplying real numbers is always defined.

The key idea is that multiplying two irrational numbers doesn’t fix the result to be one type of number. It can end up rational or irrational. For example, sqrt(2) times sqrt(2) equals 2, which is rational. But sqrt(2) times sqrt(3) equals sqrt(6), which is irrational. There are many other cases where the product is rational, like sqrt(8) times sqrt(2) equals 4. Since we can obtain both rational and irrational results, the product of two irrational numbers can be either. It’s not undefined, because multiplying real numbers is always defined.

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