Solve for a square root of 4a+4=8

$\sqrt{4 a + 4} = 8$

Step 1

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

${\sqrt{4 a + 4}}^{2} = 8^{2}$

Step 2

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{4 a + 4}$ as ${(4 a + 4)}^{\frac{1}{2}}$ .

${({(4 a + 4)}^{\frac{1}{2}})}^{2} = 8^{2}$

Simplify the left side.

Simplify ${({(4 a + 4)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(4 a + 4)}^{\frac{1}{2}})}^{2}$ .

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

${(4 a + 4)}^{\frac{1}{2} \cdot 2} = 8^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(4 a + 4)}^{\frac{1}{2} \cdot 2} = 8^{2}$

Rewrite the expression.

${(4 a + 4)}^{1} = 8^{2}$

Simplify.

$4 a + 4 = 8^{2}$

Simplify the right side.

Raise $8$ to the power of $2$ .

$4 a + 4 = 64$

Step 3

Solve for $a$ .

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

Subtract $4$ from both sides of the equation.

$4 a = 64 - 4$

Subtract $4$ from $64$ .

$4 a = 60$

Divide each term in $4 a = 60$ by $4$ and simplify.

Divide each term in $4 a = 60$ by $4$ .

$\frac{4 a}{4} = \frac{60}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 a}{4} = \frac{60}{4}$

Divide $a$ by $1$ .

$a = \frac{60}{4}$

Simplify the right side.

Divide $60$ by $4$ .

$a = 15$