Back to the basics: ... what is Root 4?

[qshyrn]

i had some calculus problem in class (although the problem wasnt really calculus if u get what i mean lol)... so it started off: (this is the first time ive done latex forgive me if i did it wrong)


now... my teacher solves this and gets 31..   but then i ask her why you cant take a negative value for the root 4 ... and she couldnt answer!
im sorta confused...  its sorta obvious for the problem that u should take root 4 as positive two ,but WHY CANT YOU TAKE IT AS -2
what is the value of root 4?

[/0]

Because by definition, denotes the positive square root. The function is only positive.
If you are asked to evaluate the answer is 2, but if you are asked to find the (edit: square) roots of 4, the answer is . The difference is in the definition.

Also, the latex for is "\left[x^2\right]_0^1"

[shinny]

and she couldnt answer!

Oh god.

WHY CANT YOU TAKE IT AS -2
what is the value of root 4?

Try graphing , and this might explain some of it. But basically, the formal definition of is that you only take the positive root. The negative root must be denoted by , and both would hence be .

EDIT: Beaten by /0.

[qshyrn]

Because by definition, denotes the positive square root. The function is only positive.
If you are asked to evaluate the answer is 2, but if you are asked to find the roots of 4, the answer is . The difference is in the definition.

Also, the latex for is "\left[x^2\right]_0^1"

hmm ok thanks..  ive always thought the root symbol means 'something times something' equals the number inside the root

[shinny]

Because by definition, denotes the positive square root. The function is only positive.
If you are asked to evaluate the answer is 2, but if you are asked to find the roots of 4, the answer is . The difference is in the definition.

Also, the latex for is "\left[x^2\right]_0^1"

hmm ok thanks..  ive always thought the root symbol means 'something times something' equals the number inside the root

Yeh, it's important to just recognise that it is a function, and hence cannot return two answers.

[qshyrn]

and she couldnt answer!

Oh god.

WHY CANT YOU TAKE IT AS -2
what is the value of root 4?

Try graphing , and this might explain some of it. But basically, the formal definition of is that you only take the positive root. The negative root must be denoted by , and both would hence be .

EDIT: Beaten by /0.

lol 'oh god' .. . yes this was a very surprising mistake by my teacher, she never gets things wrong and is VERY good at explaning things (AND SHE IS AN ASIAN TOO)

anyway i sorta cleared it up afterschool with my dad but i didnt trust him 100% so i decided to ask on vn.

[TrueTears]

Yes, I think /0 makes a really good point, there is a subtle difference between finding the square roots of something and to find .

This happens quite a lot in complex numbers.

[kamil9876]

May be a bit of topic, but sort of related to some cool shit I was thinking about today: Prove that if a polynomial with only rational coefficients, , has where is rational, then .

[NE2000]

i had some calculus problem in class (although the problem wasnt really calculus if u get what i mean lol)... so it started off: (this is the first time ive done latex forgive me if i did it wrong)


now... my teacher solves this and gets 31..   but then i ask her why you cant take a negative value for the root 4 ... and she couldnt answer!
im sorta confused...  its sorta obvious for the problem that u should take root 4 as positive two ,but WHY CANT YOU TAKE IT AS -2
what is the value of root 4?

Essentially:

Solve:


Solve:


This leads to another concept though and that is creating solutions. Essentially when you square something you can create an extra solution. Obviously this is not what you want. So for example if I had and decided to square both sides I get and then I finally get which is incorrect. So beware!