Solve for a square root of 2a+6=6

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

Step 1

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

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

Step 2

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2 a + 6}$ as ${(2 a + 6)}^{\frac{1}{2}}$ .

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

Simplify the left side.

Simplify ${({(2 a + 6)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(2 a + 6)}^{\frac{1}{2}})}^{2}$ .

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Simplify the right side.

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

$2 a + 6 = 36$

Step 3

Solve for $a$ .

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

Subtract $6$ from both sides of the equation.

$2 a = 36 - 6$

Subtract $6$ from $36$ .

$2 a = 30$

Divide each term in $2 a = 30$ by $2$ and simplify.

Divide each term in $2 a = 30$ by $2$ .

$\frac{2 a}{2} = \frac{30}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 a}{2} = \frac{30}{2}$

Divide $a$ by $1$ .

$a = \frac{30}{2}$

Simplify the right side.

Divide $30$ by $2$ .

$a = 15$