Solve 3=sqrt{p-2(3)/2}

$$3 = \sqrt { \frac { p - 2 ( 3 ) } { 2 } }$$

Solve for p

$$p=24$$

Steps for Solving Radical Equations

Multiply 2 and 3 to get 6.

$$3=\sqrt{\frac{p-6}{2}}$$

Divide each term of p-6 by 2 to get \frac{1}{2}p-3.

$$3=\sqrt{\frac{1}{2}p-3}$$

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

$$\sqrt{\frac{1}{2}p-3}=3$$

Square both sides of the equation.

$$\frac{1}{2}p-3=9$$

Add 3 to both sides of the equation.

$$\frac{1}{2}p-3-\left(-3\right)=9-\left(-3\right)$$

Subtracting -3 from itself leaves 0.

$$\frac{1}{2}p=9-\left(-3\right)$$

Subtract -3 from 9.

$$\frac{1}{2}p=12$$

Multiply both sides by 2.

$$\frac{\frac{1}{2}p}{\frac{1}{2}}=\frac{12}{\frac{1}{2}}$$

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

$$p=\frac{12}{\frac{1}{2}}$$

Divide 12 by \frac{1}{2} by multiplying 12 by the reciprocal of \frac{1}{2}.

$$p=24$$