Solve for a 12 = square root of a+108

$12 = \sqrt{a + 108}$

Step 1

Rewrite the equation as $\sqrt{a + 108} = 12$ .

$\sqrt{a + 108} = 12$

Step 2

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

${\sqrt{a + 108}}^{2} = 12^{2}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{a + 108}$ as ${(a + 108)}^{\frac{1}{2}}$ .

${({(a + 108)}^{\frac{1}{2}})}^{2} = 12^{2}$

Simplify the left side.

Simplify ${({(a + 108)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(a + 108)}^{\frac{1}{2}})}^{2}$ .

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

${(a + 108)}^{\frac{1}{2} \cdot 2} = 12^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(a + 108)}^{\frac{1}{2} \cdot 2} = 12^{2}$

Rewrite the expression.

${(a + 108)}^{1} = 12^{2}$

Simplify.

$a + 108 = 12^{2}$

Simplify the right side.

Raise $12$ to the power of $2$ .

$a + 108 = 144$

Step 4

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

Subtract $108$ from both sides of the equation.

$a = 144 - 108$

Subtract $108$ from $144$ .

$a = 36$