Solve Radical Equations

Solving Radical Equations

Dr. Tom Giles

What is a Radical?

• Radical is a term used for a square root symbol 

• And how do you solve square roots?

Multiple Choice

Solve

• {49,-49}

• {8,-8}

• {7,-7}

• No Solution

Multiple Choice

Solve using square roots.

• ±81
• ±9
• ±3
• No real solution

Multiple Choice

Solve using square roots.

• ± 1/4
• ± 9/36
• ± 1/2
• No real solution

An important note....

Always check to verify your answers 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

Multiple Choice

Solve the radical equation. Don't forget to check your answers!

• No solution

• 33

• 61

• 47

Multiple Choice

Solve the radical equation. Don't forget to check your answers!

• -5

• 5

• 10

• 25

Multiple Choice

Solve the radical equation. Don't forget to check your answers!

• 2

• 1

• -1

• 8

Multiple Choice

Solve the radical equation. Don't forget to check your answers!

• A

• B

• C

• D

Multiple Choice

Solve the radical equation. Don't forget to check your answers!

• x = -6

• x = 3

• x = 7/3

• x = -5

Multiple Choice

Solve the radical equation. Don't forget to check your answers!

• x = -6

• x = 3

• x = 7/3

• No Solution

Multiple Choice

Solve the radical equation. Don't forget to check your answers!

• x = -2

• x = 3

• x = 5

• No Solution

Multiple Choice

Solve the radical equation. Don't forget to check your answers!

• x = 2

• x = 4

• x = 7

• x = 9

Multiple Choice

Solve the radical equation. Don't forget to check your answers!

• -6

• -3

• 6

• 15

Multiple Choice

Solve the radical equation. Don't forget to check your answers!

• 104/5

• 124/5

• 25

• 14/5