Question

write both of the solutions to the following square root. give your answers as positive and negative multiples of ( i ).
( sqrt{-81} )
show your work here

Explanation:

Step1: Separate negative from radicand

$\sqrt{-81} = \sqrt{81 \times (-1)}$

Step2: Use imaginary unit definition

$\sqrt{81 \times (-1)} = \sqrt{81} \times \sqrt{-1}$

Step3: Simplify square roots

$\sqrt{81} = 9$, $\sqrt{-1} = i$, so $\sqrt{-81} = 9i$

Step4: Find negative solution

Since squaring $-9i$ also gives $-81$, the second solution is $-9i$

Answer:

$9i$ and $-9i$