Question

solve the equation.
simplify your answer as much as possible.
$b^2 = -44$
if there is more than one solution, separate them with commas.
$b = \square$

Explanation:

Step1: Take square root of both sides

To solve \( b^2 = -44 \), 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, \( b = \pm\sqrt{-44} \).

Step2: Simplify the square root

Simplify \( \sqrt{-44} \). We can rewrite \( -44 \) as \( -1 \times 44 \), so \( \sqrt{-44}=\sqrt{-1\times44}=\sqrt{-1}\times\sqrt{44} \). Since \( \sqrt{-1} = i \) and \( \sqrt{44}=\sqrt{4\times11}=2\sqrt{11} \), we have \( \sqrt{-44} = 2i\sqrt{11} \) (or \( 2\sqrt{11}i \)).

Step3: Write the solutions

Putting it all together, the solutions for \( b \) are \( b = 2i\sqrt{11}, -2i\sqrt{11} \) (or \( b = 2\sqrt{11}i, -2\sqrt{11}i \)).

Answer:

\( 2i\sqrt{11}, -2i\sqrt{11} \) (or \( 2\sqrt{11}i, -2\sqrt{11}i \))