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

1 Answer
George C.
Oct 8, 2015

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

Explanation:

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#

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