Question

Consider the statement: "An irrational number multiplied by an irrational number always makes an irrational product." Select all the examples that show that this statement is false. Responses A 4–√⋅5–√ square root of 4 times square root of 5 B 4–√⋅4–√ square root of 4 times square root of 4 C 7–√⋅7–√

Answer 1

Unfortunately your answer choices are too garbled to make much sense.

But I'll show an example where the original claim is proven false.

The numbers $\sqrt{20}$ and $\sqrt{5}$ are both irrational, but $\sqrt{20}*\sqrt{5} = \sqrt{20*5} = \sqrt{100} = 10$ is rational since 10 = 10/1.

Therefore the claim "irrational times irrational = irrational" isn't always true.