Solve Using the Square Root Property 4y^2=32

$4 y^{2} = 32$

Step 1

Divide each term in $4 y^{2} = 32$ by $4$ and simplify.

Divide each term in $4 y^{2} = 32$ by $4$ .

$\frac{4 y^{2}}{4} = \frac{32}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y^{2}}{4} = \frac{32}{4}$

Divide $y^{2}$ by $1$ .

$y^{2} = \frac{32}{4}$

Simplify the right side.

Divide $32$ by $4$ .

$y^{2} = 8$

Step 2

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

$y = \pm \sqrt{8}$

Step 3

Simplify $\pm \sqrt{8}$ .

Rewrite $8$ as $2^{2} \cdot 2$ .

Factor $4$ out of $8$ .

$y = \pm \sqrt{4 (2)}$

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

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

Pull terms out from under the radical.

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

Step 4

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.

$y = 2 \sqrt{2}$

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

$y = - 2 \sqrt{2}$

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

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$y = 2.82842712 \dots, - 2.82842712 \dots$