Solve for Z Z^2=49

$Z^{2} = 49$

Step 1

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

$Z = \pm \sqrt{49}$

Step 2

Simplify $\pm \sqrt{49}$ .

Rewrite $49$ as $7^{2}$ .

$Z = \pm \sqrt{7^{2}}$

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

$Z = \pm 7$

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.

$Z = 7$

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

$Z = - 7$

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

$Z = 7, - 7$