Solve Equations with Radicals on Both Sides

Solving Radical Equations

What is a Radical?

• Radical is a term used for a square root symbol 

An important note....

Always check your answers using a graph when working with radicals.  Sometimes you get an answer algebraically that is not in the DOMAIN of the function.  These are called extraneous solutions.

Steps to Solve a Radical Equation

• Isolate the radical.  This means move anything outside the radical to the other side of the equation by performing opposite operations.

• Square both sides

• Solve whatever is left.  This will always involve what was originally underneath the radical

• Check in Desmos

Multiple Choice

$$6=\sqrt{8-4n}$$  

• -7 and 7

• -7

• -7 and -5

• 4

Multiple Choice

$$\sqrt{\frac{x}{9}}=\sqrt{80-x}$$  

• 72 and -7

• 7

• 4

• 72

Multiple Choice

$$x-2=\sqrt{5x-14}$$  

• -8

• 8 and -8

• 6 and 3

• -8 and 6