help please (1 Viewer)

[Mark576]

I recently had my first preliminary mathematics exam and one of the questions went like this:

Choose the irrational numbers from the following list of numbers:

..., ..., ..., ..., ..., root(-6)

Would you consider this an irrational number? Do you think the teacher would regard this as irrational since we have not dealt with complex numbers before?

 

[jyu]

I recently had my first preliminary mathematics exam and one of the questions went like this:

Choose the irrational numbers from the following list of numbers:

..., ..., ..., ..., ..., root(-6)

Would you consider this an irrational number? Do you think the teacher would regard this as irrational since we have not dealt with complex numbers before?

Irrational numbers are real numbers. Since root(-6) is a complex number, .: it is not an irrational number.

 

[Mark576]

But we haven't learnt anything about complex numbers, so how the hell can they ask us to classify it as irrational or rational? We haven't touched on the concept of complex numbers, and thus have no real indication of unreal numbers. I just thought that an irrational number cannot be expressed in the form of a/b where a and b are real. Since root(-6) is complex, i.e unreal wouldn't it be impossible to express it as a/b with real numbers a and b? I have no idea ...

 

[hoca pontis]

to clear things up, root (-6) is not a real number. its not rational or irrational because it just doesnt exist. eh.. i hope that helped you..somehow..lol

 

[PC]

Cruel question I think.

 

[Mark576]

root(m^2), given that m < 0, is equal to -m right? since m is negative, once you square it and then take the square root, you'll get an answer which is positive, but it will still have the value of m, i.e. simplified it comes out to -m. right?

 

[PC]

I don't think so.

The sign for the square root, √, means the positive root.

So √4 = 2.
That's why you see +–√(b²–4ac) in the quadratic formula.

On the other hand, if you're trying to solve something like x² = 4, then you root both sides and get x = +–2.

So if your question says √(m²) then the answer will be m, regardless of whether m<0 or not.

If m is negative, when you square it, it becomes positive. And √ asks for the positive root.

 

[Mark576]

I understand what you're saying, but m is negative (i.e m = -4), which means that after we've finished with the operations we will get a postive number, regardless of the value of m. Since we are going to get a positive m, the answer must be -m, since m is originally negative, and since two negatives will give a positive. See what I mean?

 

[PC]

No.

Take m = –4.
That means that m² = 16. Right?
Therefore you're being asked to work out √16, which is 4.

Take m = 4.
That means that m² = 16. Right?
Therefore you're being asked to work out √16, which is 4.

So it doesn't matter if m was originally positive or negative. The answer is the same. √ means the positive root, so that's what you'll get.

 

[pLuvia]

root(m^2), given that m < 0, is equal to -m right? since m is negative, once you square it and then take the square root, you'll get an answer which is positive, but it will still have the value of m, i.e. simplified it comes out to -m. right?

sqrt{x²}, where x is any number
=|x|
Hence x>0 or x<0

 

[PC]

sqrt{x²}, where x is any number
=|x|
Hence x>0 or x<0

Yeah, that too.

 

[ashraf91]

at this stage it is noen as undefined only

 

[ashraf91]

so dont worry yet

 

[Zephyrio]

Irrational numbers is an element of the real number system.

So since root(-6) is complex it wouldn't be an irrational number.