Solve for y 1/3y^2-8/27=0

$\frac{1}{3} y^{2} - \frac{8}{27} = 0$

Combine $\frac{1}{3}$ and $y^{2}$ .

$\frac{y^{2}}{3} - \frac{8}{27} = 0$

Add $\frac{8}{27}$ to both sides of the equation.

$\frac{y^{2}}{3} = \frac{8}{27}$

Multiply both sides of the equation by $3$ .

$3 \frac{y^{2}}{3} = 3 (\frac{8}{27})$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$3 \frac{y^{2}}{3} = 3 (\frac{8}{27})$

Rewrite the expression.

$y^{2} = 3 (\frac{8}{27})$

Simplify the right side.

Cancel the common factor of $3$ .

Factor $3$ out of $27$ .

$y^{2} = 3 \frac{8}{3 (9)}$

Cancel the common factor.

$y^{2} = 3 \frac{8}{3 \cdot 9}$

Rewrite the expression.

$y^{2} = \frac{8}{9}$

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

$y = \pm \sqrt{\frac{8}{9}}$

Simplify $\pm \sqrt{\frac{8}{9}}$ .

Rewrite $\sqrt{\frac{8}{9}}$ as $\frac{\sqrt{8}}{\sqrt{9}}$ .

$y = \pm \frac{\sqrt{8}}{\sqrt{9}}$

Simplify the numerator.

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

Factor $4$ out of $8$ .

$y = \pm \frac{\sqrt{4 (2)}}{\sqrt{9}}$

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

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

Pull terms out from under the radical.

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

Simplify the denominator.

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

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

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

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

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.

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

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

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

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

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$y = 0.94280904 \dots, - 0.94280904 \dots$

Solve for y 1/3y^2-8/27=0

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