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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