Solve for y square root of y+(y+2)=6

$\sqrt{y + (y + 2)} = 6$

Step 1

Remove parentheses.

$\sqrt{y + y + 2} = 6$

Step 2

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{y + y + 2}}^{2} = 6^{2}$

Step 3

Simplify each side of the equation.

Remove parentheses.

$\sqrt{y + y + 2} = 6$

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{y + y + 2}}^{2} = 6^{2}$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{y + y + 2}$ as ${(y + y + 2)}^{\frac{1}{2}}$ .

${({(y + y + 2)}^{\frac{1}{2}})}^{2} = 6^{2}$

Simplify the left side.

Simplify ${({(y + y + 2)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(y + y + 2)}^{\frac{1}{2}})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(y + y + 2)}^{\frac{1}{2} \cdot 2} = 6^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(y + y + 2)}^{\frac{1}{2} \cdot 2} = 6^{2}$

Rewrite the expression.

${(y + y + 2)}^{1} = 6^{2}$

Add $y$ and $y$ .

${(2 y + 2)}^{1} = 6^{2}$

Simplify.

$2 y + 2 = 6^{2}$

Simplify the right side.

Raise $6$ to the power of $2$ .

$2 y + 2 = 36$

Step 4

Solve for $y$ .

Move all terms not containing $y$ to the right side of the equation.

Subtract $2$ from both sides of the equation.

$2 y = 36 - 2$

Subtract $2$ from $36$ .

$2 y = 34$

Divide each term in $2 y = 34$ by $2$ and simplify.

Divide each term in $2 y = 34$ by $2$ .

$\frac{2 y}{2} = \frac{34}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{34}{2}$

Divide $y$ by $1$ .

$y = \frac{34}{2}$

Simplify the right side.

Divide $34$ by $2$ .

$y = 17$

Solve for y square root of y+(y+2)=6

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