Question

Find each product. Then determine which conclusion can be drawn based on the results.

√2•√2
√5•√7
√ 2•18
√2•√6
The product of two irrational numbers is always rational.
The product of two irrational numbers can be rational or irrational.
The product of two irrational numbers is always irrational.
The product of two irrational numbers cannot be determined.

Answer 1

Second answer:

"The product of two irrational numbers can be rational or irrational"

Explanation:

notice from the first product

`√(2) \,* \,√(2) = √(4) = 2`

that the product of two irrational numbers can give us a rational one.

from the other three examples, the answer for the products always contains a square root that cannot be reduced, so they all result in an irrational number.

Then, depending on the type of irrationals used, the product can be either rational or irrational.