Solve for y 5y^2=270

$5 y^{2} = 270$

Step 1

Divide each term in $5 y^{2} = 270$ by $5$ and simplify.

Divide each term in $5 y^{2} = 270$ by $5$ .

$\frac{5 y^{2}}{5} = \frac{270}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y^{2}}{5} = \frac{270}{5}$

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

$y^{2} = \frac{270}{5}$

Simplify the right side.

Divide $270$ by $5$ .

$y^{2} = 54$

Step 2

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

$y = \pm \sqrt{54}$

Step 3

Simplify $\pm \sqrt{54}$ .

Rewrite $54$ as $3^{2} \cdot 6$ .

Factor $9$ out of $54$ .

$y = \pm \sqrt{9 (6)}$

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

$y = \pm \sqrt{3^{2} \cdot 6}$

Pull terms out from under the radical.

$y = \pm 3 \sqrt{6}$

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.

$y = 3 \sqrt{6}$

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

$y = - 3 \sqrt{6}$

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

$y = 3 \sqrt{6}, - 3 \sqrt{6}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$y = 3 \sqrt{6}, - 3 \sqrt{6}$

Decimal Form:

$y = 7.34846922 \dots, - 7.34846922 \dots$