Sqrt(2) x Sqrt(2)?

[MathsNerd203]

I know this question sounds basic, but I'm just curious...

So I did a test yesterday and the question in the title of this post appeared in the multiple choice section. Two of the options for answers were "2" or "None of the above" (I haven't included the rest because they were obviously wrong).

Now, if this was a short answer question, I would have written "plus/minus 2", but that wasn't an option, so I simply circled "2".

Should I have circled "None of the above"? Was my answer technically incorrect?

[Callum@1373]

No you should be correct 

2^.5 * 2^.5 (add the indices when multiplying) = 2^1 = 2

You wouldn't need to add the plus minus symbol, because you are not taking the square root of anything, you are simply just multiplying.

If you think about it, if you had plus minus 2, consider the -2, you would be saying that a number under one of the square root signs was a negative because that would be the only way to end up with a negative result.

But we can't have the square root of a negative number, and in your case the numbers under the square root signs were not negative 

[keltingmeith]

If you think about it, if you had plus minus 2, consider the -2, you would be saying that a number under one of the square root signs was a negative because that would be the only way to end up with a negative result.

Close - you'd actually need a negative outside one of the square roots to get -2. A negative inside one of them suggests something else. Otherwise, beautiful explanation.

[kinslayer]

I know this question sounds basic, but I'm just curious...

So I did a test yesterday and the question in the title of this post appeared in the multiple choice section. Two of the options for answers were "2" or "None of the above" (I haven't included the rest because they were obviously wrong).

Now, if this was a short answer question, I would have written "plus/minus 2", but that wasn't an option, so I simply circled "2".

Should I have circled "None of the above"? Was my answer technically incorrect?

To add to what Callum#1373 has said, square roots of real numbers are always positive. The reason why the plus/minus bit comes up is that if , say, you can't actually take the square root of both sides to get for technical reasons. Instead you do and , then apply the null factor law.