Solve Using the Square Root Property z^2=-36

$z^{2} = - 36$

Step 1

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$z = \pm \sqrt{- 36}$

Step 2

Simplify $\pm \sqrt{- 36}$ .

Rewrite $- 36$ as $- 1 (36)$ .

$z = \pm \sqrt{- 1 (36)}$

Rewrite $\sqrt{- 1 (36)}$ as $\sqrt{- 1} \cdot \sqrt{36}$ .

$z = \pm \sqrt{- 1} \cdot \sqrt{36}$

Rewrite $\sqrt{- 1}$ as $i$ .

$z = \pm i \cdot \sqrt{36}$

Rewrite $36$ as $6^{2}$ .

$z = \pm i \cdot \sqrt{6^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$z = \pm i \cdot 6$

Move $6$ to the left of $i$ .

$z = \pm 6 i$

Step 3

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$z = 6 i$

Next, use the negative value of the $\pm$ to find the second solution.

$z = - 6 i$

The complete solution is the result of both the positive and negative portions of the solution.

$z = 6 i, - 6 i$