Solve Using the Square Root Property k^2=76

$k^{2} = 76$

Step 1

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

$k = \pm \sqrt{76}$

Step 2

Simplify $\pm \sqrt{76}$ .

Rewrite $76$ as $2^{2} \cdot 19$ .

Factor $4$ out of $76$ .

$k = \pm \sqrt{4 (19)}$

Rewrite $4$ as $2^{2}$ .

$k = \pm \sqrt{2^{2} \cdot 19}$

Pull terms out from under the radical.

$k = \pm 2 \sqrt{19}$

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.

$k = 2 \sqrt{19}$

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

$k = - 2 \sqrt{19}$

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

$k = 2 \sqrt{19}, - 2 \sqrt{19}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$k = 2 \sqrt{19}, - 2 \sqrt{19}$

Decimal Form:

$k = 8.71779788 \dots, - 8.71779788 \dots$