Solve Using the Square Root Property 5y^2-35=0

$5 y^{2} - 35 = 0$

Step 1

Add $35$ to both sides of the equation.

$5 y^{2} = 35$

Step 2

Divide each term in $5 y^{2} = 35$ by $5$ and simplify.

Divide each term in $5 y^{2} = 35$ by $5$ .

$\frac{5 y^{2}}{5} = \frac{35}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y^{2}}{5} = \frac{35}{5}$

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

$y^{2} = \frac{35}{5}$

Simplify the right side.

Divide $35$ by $5$ .

$y^{2} = 7$

Step 3

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

$y = \pm \sqrt{7}$

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.

$y = \sqrt{7}$

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

$y = - \sqrt{7}$

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

$y = \sqrt{7}, - \sqrt{7}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$y = \sqrt{7}, - \sqrt{7}$

Decimal Form:

$y = 2.64575131 \dots, - 2.64575131 \dots$