Solve Using the Square Root Property 4y^2=72

$4 y^{2} = 72$

Step 1

Divide each term in $4 y^{2} = 72$ by $4$ and simplify.

Divide each term in $4 y^{2} = 72$ by $4$ .

$\frac{4 y^{2}}{4} = \frac{72}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y^{2}}{4} = \frac{72}{4}$

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

$y^{2} = \frac{72}{4}$

Simplify the right side.

Divide $72$ by $4$ .

$y^{2} = 18$

Step 2

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

$y = \pm \sqrt{18}$

Step 3

Simplify $\pm \sqrt{18}$ .

Rewrite $18$ as $3^{2} \cdot 2$ .

Factor $9$ out of $18$ .

$y = \pm \sqrt{9 (2)}$

Rewrite $9$ as $3^{2}$ .

$y = \pm \sqrt{3^{2} \cdot 2}$

Pull terms out from under the radical.

$y = \pm 3 \sqrt{2}$

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.

$y = 3 \sqrt{2}$

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

$y = - 3 \sqrt{2}$

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

$y = 3 \sqrt{2}, - 3 \sqrt{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$y = 3 \sqrt{2}, - 3 \sqrt{2}$

Decimal Form:

$y = 4.24264068 \dots, - 4.24264068 \dots$