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Radical Equations

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

To solve a radical equation, isolate the radical, square both sides, then solve. Squaring can introduce extraneous solutions, so check answers in the original equation.

What you'll learn

Why it matters: Pipe-flow formulas, pendulum-period equations, and engineering safety factors need a squared step to remove a radical. Always check candidate answers against the original equation — squaring can invent solutions that do not actually work.

Worked example

Problem. Solve sqrt(x + 5) = 4.

  1. Square both sides.
  2. x + 5 = 16.
  3. x = 11, and sqrt(16) = 4 checks.

Answer: 11

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. Solve sqrt(x) = 9.

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  1. Square both sides.

Answer: 81

2. Solve sqrt(x + 1) = 5.

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  1. x + 1 = 25.

Answer: 24

3. Solve sqrt(x - 3) = 6.

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  1. x - 3 = 36.

Answer: 39

4. Solve sqrt(2x) = 8.

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  1. 2x = 64.

Answer: 32

5. Why check radical equation solutions?

Choices: Squaring can create extraneous solutions · Square roots never have answers · All answers are negative · Checking is optional only for graphs

Show solution
  1. Squaring is not always reversible.

Answer: Squaring can create extraneous solutions

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