What is the square root of -26 times the square root of -13?

##sqrt(-26)*sqrt(-13) = -13sqrt(2)##

If ##a, b >= 0## then ##sqrt(a)sqrt(b) = sqrt(ab)##

If ##a < 0##, then ##sqrt(a) = i sqrt(-a)##, where ##i## is the imaginary unit.

So:

##sqrt(-26) * sqrt(-13) = i sqrt(26) * i sqrt(13)##

##= i^2 * sqrt(26)sqrt(13)##

##= -1 * sqrt(26*13)##

##= - sqrt(13^2 * 2)##

##= - sqrt(13^2)sqrt(2)##

##= -13sqrt(2)##

Note that you have to be careful with square roots of negative numbers. For example:

##1 = sqrt(1) = sqrt(-1 * -1) != sqrt(-1)*sqrt(-1) = i^2 = -1##