Question

Which choice is equivalent to the expression below? √-27

Answer 1

Answer:

it is 3i√3

Step-by-step explanation:

because √-27= √-9(3)= 3(-1)√3= 3i√3

Answer 2

Answer:

$\large\boxed{\sqrt{-27}=3\sqrt3 i}$

Step-by-step explanation:

$\sqrt{-27}\\\\\text{In the set of real numbers, this number does not exist.}\\\\\text{In the set of complex numbers:}\\\\i=\sqrt{-1}\\\\\sqrt{-27}=\sqrt{(27)(-1)}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\sqrt{27}\cdot\sqrt{-1}=\sqrt{9\cdot3}\cdot i=\sqrt9\cdot\sqrt3\cdot i=3\sqrt3 i$