√(-3)•√(-12) ≠ ±6 

Will do! Thank you

He said “don’t stop”, then you said “will do”, so you will stop or not? 😅

I'm confused with the "radical sign", but I'm sure it's trivial so I'll go Google it now

And it's not trivial: It's a necessity around complex numbers that prevents us from proving that 1 = -1 from the definition of the imaginary unit i

@k.o.hakala2112 I know it has a necessity, I just said that I used to have to write both "answers", but that changed.

Yeah and what I said was untrue, it's to put away with discontinuities in the complex plane.

@@k.o.hakala2112 Ok

Then quare root of what is -6?

6 and -6 don't multiply to 36

@@vidya014 Thank you. Exactly

@@lookingforahookup let me clear that up for you….6^2 and (-6)^2 both equal 36. You’re welcome 😑

@@lookingforahookup He meant "-6 and -6" not "6 and -6". The latter is not a square root so that's obviously not what he meant.

You can multiply imaginary numbers, it's just that the property of sqrt(x)*sqrt(y) = sqrt(x*y) is only valid when both x and y are positive real numbers. If either number is a negative number, you must first separately handle the negative part of x or y, and then continue simplifying the product of square roots, once you reduce it to a product of roots of positive numbers. Likewise if you start with square roots of complex numbers in general. It will be the case that in general, sqrt(x*y) and sqrt(x)*sqrt(y) will both be valid solutions for z to z^2 = x*y, but they will not strictly equal each other, due to conventions of principal roots implied by the square root function. For square roots specifically, they will either equal each other, or be negatives of each other. I'll leave it as a challenge for you, to determine what property of the original numbers would make them equal.

So is x= -6 wrong?

@@Alfakkin at least that's what they claim. interestingly enough, that would mean that equations like x²-36=0 would have only one solution ( x=√36=6 ) despite everybody knowing that any and all quadratic equations have 2 solutions. easily proven by the fact that x²-36=0 can be factored as (x+6)(x-6)=0 wich is, evidently, true for either x=6 or x=-6 so, despite what many want to claim, the square root of a number has two results. I understand why some prefer to work with the idea that the result is only the positive value. they are welcome to do so, but be very careful when doing that kind of thing.

Glad to help

Happy to help!

It's my pleasure

Didn't know i would find you here

The root sign is called a radical, and by default indicates principal square root. It of course, can indicate other roots as well. The convention for principal root: Priority 1: The positive real root Priority 2: The negative real root Priority 3: The closest root to the positive real axis. If two candidates for the principal root are a complex conjugate pair, then the positive imaginary one is the principle root.

@@carultch awsome! i learned something new.. now its a good day

b=6,-6

@mrhtutoring So, therefore, how can you say that the square root of 36 is not negative 6?

By definition, square roots of 36 are ±6. But when we use the radical sign, √, we only use the positive root. Meaning √36 is only equal to +6. When you take the sqrt of left and right side of an equation, you do add +-

By definition, square roots of 36 are ±6. But when we use the radical sign, √, we only use the positive root. Meaning √36 is only equal to +6.

@@mrhtutoring But -6 * -6 equals 36

You're right. But, we use only the principal root or the positive root when we use the sqrt symbol.

@mrhtutoring One thing that I know of is that -(6)² does equal -36

@@mrhtutoring ok. I understand your point. please, teach me. if not √, what symbol we use when we want to use all roots instead of "the principal"?

i is defined to mean the square root of -1