Solve Using the Square Root Property 5y^2=405

$5 y^{2} = 405$

Step 1

Divide each term in $5 y^{2} = 405$ by $5$ and simplify.

Divide each term in $5 y^{2} = 405$ by $5$ .

$\frac{5 y^{2}}{5} = \frac{405}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y^{2}}{5} = \frac{405}{5}$

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

$y^{2} = \frac{405}{5}$

Simplify the right side.

Divide $405$ by $5$ .

$y^{2} = 81$

Step 2

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

$y = \pm \sqrt{81}$

Step 3

Simplify $\pm \sqrt{81}$ .

Rewrite $81$ as $9^{2}$ .

$y = \pm \sqrt{9^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$y = \pm 9$

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.

$y = 9$

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

$y = - 9$

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

$y = 9, - 9$