Question

Simplify the given expression.

square root of negative 108 end root plus square root of negative 27

Answer 1

my choices are


negative 3 square root of 15

3 I square root of 15

9 I square root of 3

negative 9 square root of 3

Answer 2

This is the expression we're told to simplify:
\[\sqrt{-108}+\sqrt{-27}\] Whenever we have a negative value under a radical sign, we need to pull out a -1, whose square root is i. We then have:
\[i \sqrt{108} + i \sqrt{27}\] From the 108, we can pull out the perfect square 36 (whose square root is 6) and from the 27 we can pull out the perfect square 9 (whose square root is 3) so we can simplify this to:
\[6i \sqrt{3} + 3i \sqrt{3}\] Combine like terms and we get our answer:
\[9i \sqrt{3} \]