Square Root (1 Viewer)

[Jeo]

Hi,

This may be really simple, or it may not. Im not sure and thats why I am posting.

1) What is the definition of a square root of a number?

2) What is the square root of 36

3) Solve x^2 = 36

I have heard many theories about sqrt's and I'll tell you what I've heard after someone replies with the answers.

 

[Mathematician]

haha

haha i was thinking about the same thing today and came up with something interesting.

sqrt(x^2) =|x| by definition.

I tried to derive it and was pretty succesfull.

|z|= sqrt(x^2+y^2)
right? YES

if z=x or x+0i , hence y=0

Therefore |x|=sqrt(x^2)


haha - there

sqrt(36) =6

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

Therefore
x=+-6

Since in this case u can compare LHS with RHS as on both sides there are squares.

I hope that makes sense

 

[Jeo]

Therefore |x|=sqrt(x^2)

Ok and you say that x^2 = 36, x = +- 6.. you sqrt the left side. what do you do to the right?

 

[Mathematician]

..

Indicie rules apply for eq's like x^2= 36
x^2= sqrt[(+-6)^2]

To the power of a half gives x= +-6
I think

 

[Jeo]

isn't x^1/n = nth root?

so ^1/2 is square root

so its |z| because sqrt(36) is >= 0

how to get -6?

 

[Harimau]

Originally posted by Jesh
isn't x^1/n = nth root?

so ^1/2 is square root

so its |z| because sqrt(36) is >= 0

how to get -6?

i think its because of this rule:

|x|= Sqrt(x^2)

its a rule for absolute values. And when you consider the definition of an absolute value number, as in it measures the magniture of the point from the origin, it will make sense. The Squaring will get rid of negatives, and the sqrt will revert it back to x. But if you reverse it, by squaring first, and getting it into the form (+-x)^(1/2)... then the answer is (+- x)

 

[Jeo]

ok

 

[aspect]

unless you really want to, dont think too much about stuff like this

 

[Jeo]

Ok

 

[ezzy85]

I dont know if this is related, but i was wondering:

sqrt(-1) * sqrt(-1) = sqrt(-1 * -1) = sqrt(1) = 1

but

sqrt(-1) * sqrt(-1) = i² = -1

hows that work?

 

[Jeo]

Real Patel's intro to cn's i think its in there.. or I saw it in some book.. can't remember which one

 

[KeypadSDM]

Originally posted by ezzy85
sqrt(-1) * sqrt(-1) = sqrt(-1 * -1) = sqrt(1) = 1

You cannot legitimately perform that.

in doing so you have forgotten to take out the negative

it's effectively doing x = Sqrt[x^2]
.: x = -x

And for the rest of the problem

why not make it really easy on yourselves...

x^2 = 36
x^2 - 36 = 0
(x - 6)(x + 6) = 0
x = -+ 6

exactly as you would approach a roots of unity question.

 

[The Oracle]

By definition:
A square root is a number that when multiplied by itself equals a given number

Therefore, the square root of 36, can be 6 or -6.

1: 6 * 6 = 36

2: (-6) * (-6) = 36

Originally posted by Jesh
Ok and you say that x^2 = 36, x = +- 6.. you sqrt the left side. what do you do to the right?

As KeypadSDM already pointed out:

x^2 = 36
x^2 - 36 = 0
(x - 6)(x + 6) = 0
x = -+ 6

Gives the same answer if you square root the left & right side to get (x).

Hope this helps...

 

[Mathematician]

..

Oracle i think u have learnt incorrectly . lol

If u have sqrt(36) it = + 6 by definition ( |x| = + sqrt(x^2) )

like if u let x^2 = 36
|x| = +sqrt(36)= 6

then x= 6 or x=-6

that might make more sense.

I should have said that earlier. lol

 

[The Oracle]

By DICTIONARY definition:
A square root is a number that when multiplied by itself equals a given number

And how do you get |x| = sqrt(x^2)? And from what book definition? What we are discussing here is what square root actually does. so you can't assume |x| = sqrt anything unless you prove what sqrt is in the first place.

And from what definition is: sqrt(36) it = + 6 ??? From what mathematical, or otherwise, dictionary did you get this from?

I know, this is what some of my friends say.. But where did you get it from? And I think this is why this topic was started in the first place.

I hope you understand.

 

[bobo123]

i think my teacher said something about it only being the positive one
not sure though

 

[The Oracle]

Yes,

Alot of people suggest that it is + & -. Also, alot of people suggest that it is only positive.

Well, what is the reason? Why should it be + & - or only +?

I checked the dictionary, and I already posted it. And the dictionary suggests that it is + & -.

Maybe a mathematical, or scientific dictionary would explain it better. Im not sure. I don't have one.

 

[DA]

MathWorld's entry on the square root may be of interest.

 

[The Oracle]

So it is negative and positive.

Interesting Resource, Thanks for the link!

 

[The Oracle]

hmm, but in general usage, it is > or = 0...

What a weird world we live in..