Solve w=sqrt{1-k/3}

$$w = \sqrt { \frac { 1 - k } { 3 } }$$

Solve for k

$$k=1-3w^{2}$$

$$w\geq 0$$

Steps for Solving Radical Equations

Divide each term of 1-k by 3 to get \frac{1}{3}-\frac{1}{3}k.

$$w=\sqrt{\frac{1}{3}-\frac{1}{3}k}$$

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

$$\sqrt{\frac{1}{3}-\frac{1}{3}k}=w$$

Square both sides of the equation.

$$-\frac{1}{3}k+\frac{1}{3}=w^{2}$$

Subtract \frac{1}{3} from both sides of the equation.

$$-\frac{1}{3}k+\frac{1}{3}-\frac{1}{3}=w^{2}-\frac{1}{3}$$

Subtracting \frac{1}{3} from itself leaves 0.

$$-\frac{1}{3}k=w^{2}-\frac{1}{3}$$

Multiply both sides by -3.

$$\frac{-\frac{1}{3}k}{-\frac{1}{3}}=\frac{w^{2}-\frac{1}{3}}{-\frac{1}{3}}$$

Dividing by -\frac{1}{3} undoes the multiplication by -\frac{1}{3}.

$$k=\frac{w^{2}-\frac{1}{3}}{-\frac{1}{3}}$$

Divide w^{2}-\frac{1}{3} by -\frac{1}{3} by multiplying w^{2}-\frac{1}{3} by the reciprocal of -\frac{1}{3}.

$$k=1-3w^{2}$$

Solve for w

$$w=\frac{\sqrt{3-3k}}{3}$$

$$k\leq 1$$