Solve Using the Square Root Property t^2=50

$t^{2} = 50$

Step 1

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

$t = \pm \sqrt{50}$

Step 2

Simplify $\pm \sqrt{50}$ .

Rewrite $50$ as $5^{2} \cdot 2$ .

Factor $25$ out of $50$ .

$t = \pm \sqrt{25 (2)}$

Rewrite $25$ as $5^{2}$ .

$t = \pm \sqrt{5^{2} \cdot 2}$

Pull terms out from under the radical.

$t = \pm 5 \sqrt{2}$

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.

$t = 5 \sqrt{2}$

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

$t = - 5 \sqrt{2}$

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

$t = 5 \sqrt{2}, - 5 \sqrt{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$t = 5 \sqrt{2}, - 5 \sqrt{2}$

Decimal Form:

$t = 7.07106781 \dots, - 7.07106781 \dots$