What is the square root of 9? (1 Viewer)

[HSC2014]

I'm having trouble mapping out the difference between principal (positive) square roots and... square roots.
E.g. The principal square root of 9 = 3, however -3,3 are square roots of 9. CONFUSING?
I was messing around with equations in my head when i stumbled upon root (x^2) = +-x then i wondered root (3^2) = +- 3?
Say the question was to solve root 9, do i answer +- 3 or just 3? How do I know if they're referring to the principal or normal square root!?

 

[Menomaths]

You use the plus minus sign whenever you square root a number?

 

[HSC2014]

Yeah I don't think you understood my whole dilemma...

 

[Menomaths]

I know...I was going to edit that in lol...I'll just back away from the maths forum...

 

[Sy123]

I'll answer this to the best of my knowledge

Principal square root or positive square root is as its name suggests the positive number which when squared gets that new number.
When you do complex numbers, there will be a question saying: 'Find the square roots of 5+2i', there is no concept of positive and negative in complex numbers so there are 2 answers.

If they ask you to simplify:



We take the positive square root.

The difference between this and solving an equation like



The difference here is that we are being asked for what values of x satisfies this equation
x=3, and x=-3 satisfy this equation because:



So we have 2 solutions, just like we have 2 solutions for:



x=1 is a solution, so is x=2 so they are both solutions since the equation, much like 3,-3 is the solution of x^2 = 9

Hope that helped

 

[HSC2014]

Yes that cleared a lot up Thank you! I don't know why I always find myself questioning these types of things

 

[braintic]

BTW, I believe the main reason for taking only the positive square root is so that y=sqrt(x) can be defined as a FUNCTION.

 

[HSC2014]

Ah, good point