simplifying radicals - all variables

[prooftheory]

assuming all variables are simplest radicals
if sqrt(a) * sqrt(b) = c(sqrt)d
then what's the process for explaining how c and d relate to a and b?

 

[Denis]

square both sides: ab = c^2 d

 

[prooftheory]

thanks, Denis. I'm hoping to find out what the relationship between the two pair of variables has to be: sqrt(a) * sqrt(b) = c radicand d
they're all in simplified form
it's more of a logic question than a formula to solve for an answer

 

[mmm4444bot]

… all variables are simplest radicals This looks like a misstatement, to me.

Are you trying to say, instead, "Assume that all radicals are simplified." ?



… c(sqrt)d << Did you intend to change radical notation, here?

Perhaps, you mean c * sqrt(d), instead.

… sqrt(a) * sqrt(b) = c radicand d … This does not make sense, either.

(Perhaps, you misunderstand the definition of the noun radicand.)

Are you trying to state c * sqrt(d) ?



… it's more of a logic question than a formula to solve for an answer

I do not read Denis' post as a "formula to solve for an answer".

I read Denis' post as one possible explanation of how the variables a and b relate to the variables c and d (assuming that Denis interpreted your typing correctly; I'm still not sure what you're trying to ask).