Solve for a square root of a-b+c=3

$\sqrt{a - b + c} = 3$

Step 1

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

${\sqrt{a - b + c}}^{2} = 3^{2}$

Step 2

Simplify each side of the equation.

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

${({(a - b + c)}^{\frac{1}{2}})}^{2} = 3^{2}$

Simplify the left side.

Simplify ${({(a - b + c)}^{\frac{1}{2}})}^{2}$ .

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

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

${(a - b + c)}^{\frac{1}{2} \cdot 2} = 3^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(a - b + c)}^{\frac{1}{2} \cdot 2} = 3^{2}$

Rewrite the expression.

${(a - b + c)}^{1} = 3^{2}$

Simplify.

$a - b + c = 3^{2}$

Simplify the right side.

Raise $3$ to the power of $2$ .

$a - b + c = 9$

Step 3

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

Add $b$ to both sides of the equation.

$a + c = 9 + b$

Subtract $c$ from both sides of the equation.

$a = 9 + b - c$