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Radical Expressions and Equations

A free College Algebra lesson from the “Exponents and Radicals” unit, with a worked example and practice problems including step-by-step solutions.

Radicals simplify by factoring out perfect squares. Radical equations often require isolating the radical and squaring both sides, then checking solutions.

What you'll learn

Why it matters: Distance formulas, free-fall time, standard deviation, and square-root models all use radicals. Simplifying exposes perfect-square structure, while checking after squaring protects against extraneous answers.

Worked example

Problem. Solve sqrt(x + 5) = 6.

  1. Square both sides: x + 5 = 36.
  2. Subtract 5.
  3. x = 31.

Answer: 31

Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.

Practice problems

1. Simplify sqrt(50).

Show solution
  1. 50 = 25 x 2.

Answer: 5sqrt(2)

2. Solve sqrt(x - 4) = 7.

Show solution
  1. x - 4 = 49.

Answer: 53

3. Simplify sqrt(72).

Show solution
  1. 72 = 36 x 2.

Answer: 6sqrt(2)

4. Simplify sqrt(48).

Show solution
  1. 48 = 16 x 3.

Answer: 4sqrt(3)

5. Solve sqrt(x) = 9.

Show solution
  1. Square both sides.

Answer: 81

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