How do you simplify #sqrt(-3) + sqrt(-27)#?

1 Answer
George C.
Nov 27, 2015

#sqrt(-3)+sqrt(-27) = 4sqrt(3)i#

Explanation:

If #x < 0# then #sqrt(x) = (sqrt(-x))i#

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

So:

#sqrt(-3)+sqrt(-27)#

#=(sqrt(3))i + (sqrt(27))i#

#=(sqrt(3)+sqrt(27))i#

#=(sqrt(3)+sqrt(3^2*3))i#

#=(sqrt(3)+sqrt(3^2)sqrt(3))i#

#=(1sqrt(3)+3sqrt(3))i#

#=4sqrt(3)i#

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