Example 1

A quick battle with ChatGPT to try to get it to simplify $square root of (3 minus 2 Times Square root of 2)$ into the form $a + b Times Square root of 2$ .

Opening question

Asking ChatGPT Write (3 - 2*2^(0.5))^(0.5) in the form a + b*2^(0.5

The answer is wrong; ChatGPT didn't read the question correctly. So we ask it again.

Asking ChatGPT Are you sure that is correct?

ChatGPT tries again, and fails again.Feeling sorry for it, we give it another go.

Asking ChatGPT Erm. I still not sure that is correct

OK. It is being nice so we give it the question again.

OK. Here is the question again Write (3 - 2*2^(0.5))^(0.5) in the form a + b*2^(0.5)

Well this looks better, it looks like an answer. But it is wrong, the answer is actually $root 2 minus 1$ and not $1 minus root 2$

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