Solve Using the Square Root Property m^2=98

$m^{2} = 98$

Step 1

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

$m = \pm \sqrt{98}$

Step 2

Simplify $\pm \sqrt{98}$ .

Rewrite $98$ as $7^{2} \cdot 2$ .

Factor $49$ out of $98$ .

$m = \pm \sqrt{49 (2)}$

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

$m = \pm \sqrt{7^{2} \cdot 2}$

Pull terms out from under the radical.

$m = \pm 7 \sqrt{2}$

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.

$m = 7 \sqrt{2}$

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

$m = - 7 \sqrt{2}$

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

$m = 7 \sqrt{2}, - 7 \sqrt{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$m = 7 \sqrt{2}, - 7 \sqrt{2}$

Decimal Form:

$m = 9.89949493 \dots, - 9.89949493 \dots$