Question

solve $w^2 = -81$. simplify your answer as much as possible. if there is more than one solution, separate them with commas. $w = \square$

Explanation:

Step1: Take square root of both sides

To solve \( w^2 = -81 \), we take the square root of both sides. Remember that the square root of a negative number involves the imaginary unit \( i \), where \( i^2=-1 \). So, \( w=\pm\sqrt{-81} \).

Step2: Simplify the square root

We know that \( \sqrt{-81}=\sqrt{81\times(-1)}=\sqrt{81}\times\sqrt{-1} \). Since \( \sqrt{81} = 9 \) and \( \sqrt{-1}=i \), we have \( \sqrt{-81}=9i \). So the solutions for \( w \) are \( 9i,-9i \).

Answer:

\( 9i, -9i \)