Solve m=1/2sqrt{n-1}

$$m = \frac { 1 } { 2 } \sqrt { n - 1 }$$

Solve for n

$$n=4m^{2}+1$$

$$m\geq 0$$

Steps for Solving Radical Equations

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

$$\frac{1}{2}\sqrt{n-1}=m$$

Multiply both sides by 2.

$$\frac{\frac{1}{2}\sqrt{n-1}}{\frac{1}{2}}=\frac{m}{\frac{1}{2}}$$

Dividing by \frac{1}{2} undoes the multiplication by \frac{1}{2}.

$$\sqrt{n-1}=\frac{m}{\frac{1}{2}}$$

Divide m by \frac{1}{2} by multiplying m by the reciprocal of \frac{1}{2}.

$$\sqrt{n-1}=2m$$

Square both sides of the equation.

$$n-1=4m^{2}$$

Add 1 to both sides of the equation.

$$n-1-\left(-1\right)=4m^{2}-\left(-1\right)$$

Subtracting -1 from itself leaves 0.

$$n=4m^{2}-\left(-1\right)$$

Subtract -1 from 4m^{2}.

$$n=4m^{2}+1$$

Solve for m

$$m=\frac{\sqrt{n-1}}{2}$$

$$n\geq 1$$