Solve 61/9=sqrt{c-2^2/9}

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

Solve for c

$$c = \frac{3061}{9} = 340\frac{1}{9} \approx 340.111111111$$

Steps for Solving Radical Equations

Multiply both sides of the equation by 9.

$$6\times 9+1=9\sqrt{\frac{c-2^{2}}{9}}$$

Multiply 6 and 9 to get 54.

$$54+1=9\sqrt{\frac{c-2^{2}}{9}}$$

Add 54 and 1 to get 55.

$$55=9\sqrt{\frac{c-2^{2}}{9}}$$

Calculate 2 to the power of 2 and get 4.

$$55=9\sqrt{\frac{c-4}{9}}$$

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

$$55=9\sqrt{\frac{1}{9}c-\frac{4}{9}}$$

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

$$9\sqrt{\frac{1}{9}c-\frac{4}{9}}=55$$

Divide both sides by 9.

$$\sqrt{\frac{1}{9}c-\frac{4}{9}}=\frac{55}{9}$$

Square both sides of the equation.

$$\frac{1}{9}c-\frac{4}{9}=\frac{3025}{81}$$

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

$$\frac{1}{9}c-\frac{4}{9}-\left(-\frac{4}{9}\right)=\frac{3025}{81}-\left(-\frac{4}{9}\right)$$

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

$$\frac{1}{9}c=\frac{3025}{81}-\left(-\frac{4}{9}\right)$$

Subtract -\frac{4}{9} from \frac{3025}{81} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$\frac{1}{9}c=\frac{3061}{81}$$

Multiply both sides by 9.

$$\frac{\frac{1}{9}c}{\frac{1}{9}}=\frac{\frac{3061}{81}}{\frac{1}{9}}$$

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

$$c=\frac{\frac{3061}{81}}{\frac{1}{9}}$$

Divide \frac{3061}{81} by \frac{1}{9} by multiplying \frac{3061}{81} by the reciprocal of \frac{1}{9}.

$$c=\frac{3061}{9}$$