Solve 6(1/9)=sqrt{c-2^2/9}

$$6 ( \frac { 1 } { 9 } ) = \sqrt { \frac { c - 2 ^ { 2 } } { 9 } }$$

Solve for c

$$c=8$$

Steps for Solving Radical Equations

Multiply 6 and \frac{1}{9} to get \frac{6}{9}.

$$\frac{6}{9}=\sqrt{\frac{c-2^{2}}{9}}$$

Reduce the fraction \frac{6}{9} to lowest terms by extracting and canceling out 3.

$$\frac{2}{3}=\sqrt{\frac{c-2^{2}}{9}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{2}{3}=\sqrt{\frac{c-4}{9}}$$

Divide each term of c-4 by 9 to get \frac{1}{9}c-\frac{4}{9}.

$$\frac{2}{3}=\sqrt{\frac{1}{9}c-\frac{4}{9}}$$

Swap sides so that all variable terms are on the left hand side.

$$\sqrt{\frac{1}{9}c-\frac{4}{9}}=\frac{2}{3}$$

Square both sides of the equation.

$$\frac{1}{9}c-\frac{4}{9}=\frac{4}{9}$$

Add \frac{4}{9} to both sides of the equation.

$$\frac{1}{9}c-\frac{4}{9}-\left(-\frac{4}{9}\right)=\frac{4}{9}-\left(-\frac{4}{9}\right)$$

Subtracting -\frac{4}{9} from itself leaves 0.

$$\frac{1}{9}c=\frac{4}{9}-\left(-\frac{4}{9}\right)$$

Subtract -\frac{4}{9} from \frac{4}{9} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$\frac{1}{9}c=\frac{8}{9}$$

Multiply both sides by 9.

$$\frac{\frac{1}{9}c}{\frac{1}{9}}=\frac{\frac{8}{9}}{\frac{1}{9}}$$

Dividing by \frac{1}{9} undoes the multiplication by \frac{1}{9}.

$$c=\frac{\frac{8}{9}}{\frac{1}{9}}$$

Divide \frac{8}{9} by \frac{1}{9} by multiplying \frac{8}{9} by the reciprocal of \frac{1}{9}.

$$c=8$$