Solve Using the Square Root Property y^2=40

$y^{2} = 40$

Step 1

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

$y = \pm \sqrt{40}$

Step 2

Simplify $\pm \sqrt{40}$ .

Rewrite $40$ as $2^{2} \cdot 10$ .

Factor $4$ out of $40$ .

$y = \pm \sqrt{4 (10)}$

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

$y = \pm \sqrt{2^{2} \cdot 10}$

Pull terms out from under the radical.

$y = \pm 2 \sqrt{10}$

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.

$y = 2 \sqrt{10}$

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

$y = - 2 \sqrt{10}$

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

$y = 2 \sqrt{10}, - 2 \sqrt{10}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = 2 \sqrt{10}, - 2 \sqrt{10}$

Decimal Form:

$y = 6.32455532 \dots, - 6.32455532 \dots$