Solve Using the Square Root Property (9y+8)^2=48

${(9 y + 8)}^{2} = 48$

Step 1

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

$9 y + 8 = \pm \sqrt{48}$

Step 2

Simplify $\pm \sqrt{48}$ .

Rewrite $48$ as $4^{2} \cdot 3$ .

Factor $16$ out of $48$ .

$9 y + 8 = \pm \sqrt{16 (3)}$

Rewrite $16$ as $4^{2}$ .

$9 y + 8 = \pm \sqrt{4^{2} \cdot 3}$

Pull terms out from under the radical.

$9 y + 8 = \pm 4 \sqrt{3}$

Step 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.

$9 y + 8 = 4 \sqrt{3}$

Subtract $8$ from both sides of the equation.

$9 y = 4 \sqrt{3} - 8$

Divide each term in $9 y = 4 \sqrt{3} - 8$ by $9$ and simplify.

Divide each term in $9 y = 4 \sqrt{3} - 8$ by $9$ .

$\frac{9 y}{9} = \frac{4 \sqrt{3}}{9} + \frac{- 8}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 y}{9} = \frac{4 \sqrt{3}}{9} + \frac{- 8}{9}$

Divide $y$ by $1$ .

$y = \frac{4 \sqrt{3}}{9} + \frac{- 8}{9}$

Simplify the right side.

Move the negative in front of the fraction.

$y = \frac{4 \sqrt{3}}{9} - \frac{8}{9}$

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

$9 y + 8 = - 4 \sqrt{3}$

Subtract $8$ from both sides of the equation.

$9 y = - 4 \sqrt{3} - 8$

Divide each term in $9 y = - 4 \sqrt{3} - 8$ by $9$ and simplify.

Divide each term in $9 y = - 4 \sqrt{3} - 8$ by $9$ .

$\frac{9 y}{9} = \frac{- 4 \sqrt{3}}{9} + \frac{- 8}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 y}{9} = \frac{- 4 \sqrt{3}}{9} + \frac{- 8}{9}$

Divide $y$ by $1$ .

$y = \frac{- 4 \sqrt{3}}{9} + \frac{- 8}{9}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{4 \sqrt{3}}{9} + \frac{- 8}{9}$

Move the negative in front of the fraction.

$y = - \frac{4 \sqrt{3}}{9} - \frac{8}{9}$

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

$y = \frac{4 \sqrt{3}}{9} - \frac{8}{9}, - \frac{4 \sqrt{3}}{9} - \frac{8}{9}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = \frac{4 \sqrt{3}}{9} - \frac{8}{9}, - \frac{4 \sqrt{3}}{9} - \frac{8}{9}$

Decimal Form:

$y = - 0.11908852 \dots, - 1.65868924 \dots$

Solve Using the Square Root Property (9y+8)^2=48

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