How to Multiply Two Numbers with Negative Signs inside the Square Roots

How to Multiply Two Numbers with Negative Signs inside the Square Roots

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[jan-willemreens]

...What I always do in these situations is to replace all minus signs under the square roots with i^2 and then continue the algebraic calculations according to the normal rules. (Sqrt(i^2)=i and i*i=i^2=-1)----> Sqrt(-5)=Sqrt(5i^2)=iSqrt(5) and Sqrt(-15)=Sqrt(15i^2)=iSqrt(15), so

[MrMaggart]

I get why this works, but why must you simplify the square root first? I have checked three different levels of math texts and none describe the product property as one radicand must be positive. Is there a "must" for this, or is it just a because we said so? I see that you get different answers if you don't simplify the i out first, but why must you? Why is one more correct than the other?

[sabyasachidash]

Why one of the numbers has to be positive to apply that rule? What's the reason actually?

[ryanalnaser]

thanks for anything and sorry in case I did not do what I was about to do

[hacker]

If you broke apart the sqrt -15 to sqrt -5 × 3 you would have gotten the answer in two steps basically. Because sqrt -5 × sqrt -5 × sqrt 3 = -5 sqrt 3

[krunoslavregvar]

Wonderful explanation, although, I am in aqward position, meaning it is true, but, if you put it like this:
=5√5; or not? I am not sure about this...

[nandanasasikumar]

Uhm what to do in the case where one is positive and the other, negative?
Not sure if this is being clarified in the video...

[marytredinnick]

Why does the negative i squared turn back into negative 1?

[pfever]

I think both a and b must be positive not at least one of them...

[billmorrigan]

A little remark: Only the product of principal roots and the product of non-principal roots were found, not the product of the principal root and non-principal root - the latter is positive √75.

[frankargenti]

thanks to you tube you will never read this message but let s hope .... Can you explain why tho? using the polar form with Cartesian coordinates??

[allenofatlanta]

I thought that "i sqrt" equals +1?