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Homework: Radical Equations

Module by: Kenny M. Felder. E-mail the author

Summary: This module provides practice problems related to radical equations.

For each of the following, you will first identify it as one of three types of problem:

  • No x x under a radical, so don’t square both sides.
  • x x under a radical, so you will have to isolate it and square both sides.
  • More than one x x under a radical, so you will have to isolate-and-square more than once!

Then you will solve it; and finally, you will check your answers (often on a calculator). Remember that if you squared both sides, you may get false answers even if you did the problem correctly! If you did not square both sides, a false answer means you must have made a mistake somewhere.

Exercise 1

x = -3 x =-3

  • a. Which type of problem is it?
  • b. Solve for x x.
  • c. Check your answer(s).

Exercise 2

2 x - 3 = 3 x 2 x-3= 3 x

  • a. Which type of problem is it?
  • b. Solve for x x.
  • c. Check your answer(s).

Exercise 3

x - 2 x = 4 x- 2 x =4

  • a. Which type of problem is it?
  • b. Solve for x x.
  • c. Check your answer(s).

Exercise 4

4 x + 2 - 2 x = 1 4 x + 2 - 2 x =1

  • a. Which type of problem is it?
  • b. Solve for x x.
  • c. Check your answer(s).

Exercise 5

3 - x - 2 = -4 3- x - 2 =-4

  • a. Which type of problem is it?
  • b. Solve for x x.
  • c. Check your answer(s).

Exercise 6

x + 2 x = 15 x+2 x =15

  • a. Which type of problem is it?
  • b. Solve for x x.
  • c. Check your answer(s).

Exercise 7

x + 4 + x = 2 x + 4 + x =2

  • a. Which type of problem is it?
  • b. Solve for x x.
  • c. Check your answer(s).

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