Square Root (1 Viewer)

[wogboy]

As far as I know, the square root (note singular use of ROOT) of a real number refers to the number that multiplies by itself to give the original number and is greater than or equal to 0 (e.g. the square root of 9 is 3). The positive root is taken by convention, unless othwerise specified. To specify the root that is negative, simply write a negative sign in front of the square root, or say the negative square root.

However, the square roots (plural) of a number (over either the complex or real field) are the two numbers that multiply by themselves to give the original number (e.g. the square roots of 9 are 3 and -3, and also the square roots of 2i are 1 + i and -1 - i).

I'm also pretty sure that the square root (singular) of any number over the complex field doesn't properly make sense without further information (e.g. the square root of z, with the positive real part).

 

[ND]

Although this has already been cleared up, i just thought i'd add something: a number to the nth power has n roots, .'. a number always has 2 square roots.

 

[Mathematician]

...

so i didnt make sense to anyone?

 

[MiuMiu]

ppl you need to get out more

Nah Im just jealous at the size of your brains!!!!

 

[The Oracle]

We are talking about Square Roots

In the 4U forum

 

[MiuMiu]

wat are you telling me your doing 4u but you aren't smart????

 

[The Oracle]

Originally posted by YEAR12
wat are you telling me your doing 4u but you aren't smart????

Presicely.

 

[MiuMiu]

oh ok well have fun failing then dumbass doing 4u

 

[The Oracle]

hmm yeah ok!

 

[KeypadSDM]

Re: ...

Originally posted by Mathematician
so i didnt make sense to anyone?

Your statement is close to correct.
But this threw me:

(x)^2=36= sqrt[(+-6)^2]

Therefore
x=+-6

Unfortunately you cannot derive what x equals from that formula since Sqrt[x] = x^0.5 NOT +-x^0.5\
However you can derive it implicitly. So it is effectively correct...

On a completely different topic: I like my definitions:

Sqrt[2] is the only positive real whose inverse is equal to half of itself.
Pi the circumference of a circle of diameter 1.

 

[wogboy]

On a completely different topic: I like my definitions:

Sqrt[2] is the only positive real whose inverse is equal to half of itself.

Yep, but I prefer my definition of sqrt(2) being the only positive number multiplying by itself to give 2 (also sqrt(2) can be geometrically defined as length of the hypoteneus of an isosceles triangle, that has the other two sides being 1 unit in length).

Pi the circumference of a circle of diameter 1.

Great geometric definition of Pi

My favourite definition of pi would be the arithmetic one:

Pi = 4 * (1 - 1/3 + 1/5 - 1/7 + 1/9 + ... )

or

4 * {sum of ([-1]^n)/(1 - 2n) from n = 1 to n=infinity}