why square root cannot be negative?

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Rinsed

A square root is ALWAYS positive or negative.

However, in many cases its easiest to just ignore the negative option, such as simple maths or everyday situations, where the negative option is either clearly irrelevant, or you're just too lazy to bother about it.

If it is always true then why doesn't SQRT -1 = +i or -i

Reply 61

Stratos

Square root= positive

X^1/2= positive or negative

Sqrt-1=i

That should do it I guess

Reply 62

Simplicity

Not quite Stratos.

See when you square root i you need to introduce another number.

So you

k=\sqrt{i}

See nothing squares to i. So you need to make a new number up called hypercomplex numbers.

Sadly, you won't here about them till second year of uni, but they exist.

Reply 63

Slumpy

Simplicity

Not quite Stratos.

See when you square root i you need to introduce another number.

So you

k=\sqrt{i}

See nothing squares to i. So you need to make a new number up called hypercomplex numbers.

Sadly, you won't here about them till second year of uni, but they exist.

[(1+i)/2]^2=i

Reply 64

Sanjetti

It depends quite a lot on the context.

For example, with inequalities like x^2>4, you have to take into account the +ve AND -ve root, i.e. x>2 or x<-2. With most "pure" maths questions you'll have to use both

The instances where you only have to take into account the positive root is for applied or practical situations in the maths exam. For example when you have to square root a value to find out its length or to find the cost of something, you only take the positive value. Obviously this is because you can't have negative length or negative money- you just have to use your common sense. So for example if you're asked to find the radius of a circle given that its area is 5cm^2, you square root 5/pi and only take the positive root.

Reply 65

rnd

Slumpy

[(1+i)/2]^2=i

(\frac{1+i}{\sqrt{2}})^2=i

Reply 66

sporean

joseph2008

hey guys, thers this doubt i have, sometimes when you square root a number the answer is only positive but other times it can be positive or negative. the positive or negative makes more sense to me. why is the other one only positive? :confused:

There is something that my teacher said that made sense a long time ago but i forgot what they said... any help'd be appreciated :smile:

x^2 = k
x = +- sqrt(k)

On the other hand,

sqrt(x) = c

In other words, if you're given a squared variable which you're supposed to find, positive and negative. If you're getting the square root of something, just positive.

Reply 67

rnd

Simplicity

See nothing squares to i. So you need to make a new number up called hypercomplex numbers.

I hope that's meant to be a joke.

Reply 68

harr

Simplicity

Not quite Stratos.

See when you square root i you need to introduce another number.

So you

See nothing squares to i. So you need to make a new number up called hypercomplex numbers.

Sadly, you won't here about them till second year of uni, but they exist.

Your jokes are improving.

Reply 69

Slumpy

rnd

(\frac{1+i}{\sqrt{2}})^2=i

In fairness, I was quite drunk.

Reply 70

Zhen Lin

Kolya

I believe it's just a matter of convention. There's no clever reason behind it.

It's a good convention though. It behaves nicely:

\sqrt{x} \sqrt{y} = \sqrt{x y}

, when everything is positive.

x \mapsto \sqrt{x}

is a bijection on non-negative numbers.

If we defined

\sqrt{x}

to be non-positive for positive numbers, we wouldn't have the multiplicative property.

Reply 71

Torresisagod

LazyWorseThanInfidel

ive just done as levels and only just decided to do further maths, so after the exams i have learned c3, started c4 and fp1 with the help of my teacher,
i wont see her until august so im on my own until then after this friday

what you wana do in uni?

Why have you learned C3 and started C4? Surely you'll just do those next year for the A2 part of your normal maths in school?

Reply 72

LazyWorseThanInfidel

Carter_C

Why have you learned C3 and started C4? Surely you'll just do those next year for the A2 part of your normal maths in school?

for further maths you need to know some stuff that is in c3 and c4 so im preparing

il be doing c3 and c4 exams next year too but il be concentrating on as and a2 further maths

my college dont officially do further maths so il only get 2 hours a week teaching for both as and a2 further(that is one hour a week of each)

il be sitting in the a2 maths class for 4.5 hours a week in which i will do further on my own or with 2 other people

get my plan?

Reply 73

Torresisagod

LazyWorseThanInfidel

:/ Seems a bit silly to me to self-teach C3 and C4 when you're going to do it in school anyway- would be more efficient to just do the further maths modules and look at C3 and C4 as and when you need it.
Each to their own I guess.
I'm self teaching the whole further maths in a year too I think, just going to do D1 and some S1 over summer, then some/all of FP1 by January, ready to do FP2, FP3 and D2/M3 in the summer and FP1 in summer if I haven't done that in January.