# Worksheet: Radical Equations

In this worksheet, we will practice solving equations that include radical expressions, where the variable is the radicand, by raising each side to a power.

**Q5: **

Find the solution set of the equation , given that .

- A
- B
- C
- D
- E

**Q7: **

Given that , find the value of .

- A900
- B30
- C324
- D27,000

**Q8: **

For what value of is introduced as an extraneous solution to the equation when it is solved in the natural way?

**Q9: **

In order to solve the equation , Michael started with

What solutions did Michael find?

**Q11: **

Solve .

**Q12: **

Find the value of given that .

- A30
- B100
- C10
- D1,000
- E

**Q13: **

Solve .

- A
- B
- C
- D
- E

**Q14: **

Find the solution set of in .

- A
- B
- C
- D

**Q15: **

Solve .

**Q16: **

Solve .

**Q17: **

Consider the following argument for solving :

- .

What mistake was made?

- Asquaring does not give 9
- Bnot checking for extraneous solutions

**Q18: **

Find the solution set of the equation given that .

- A
- B
- C
- D
- E

**Q19: **

Solve .

**Q20: **

Given that , find the value of .

- A
- B
- C
- D

**Q22: **

Solve .

- A
- B
- C
- D
- E

**Q24: **

Daniel starts to solve as follows:

Finish the solution for him.

- A
- B
- C
- D
- E

**Q25: **

Squaring both sides of introduces an extraneous solution. What is that extraneous solution?

- A
- B
- C
- D
- E