Solving Radical Equations

Solving Radical Equations

Student Outcomes

• Students develop facility in solving radical equations.

New York State Common Core Math Algebra II, Module 1, Lesson 29

Worksheets for Algebra 2

Classwork

Example 1

Solve the equation 6 = 𝑥 + √𝑥.

Exercises 1–4

Solve.

1. 3𝑥 = 1+ 2√𝑥
2. 3 = 4√𝑥 − 𝑥
3. √𝑥 + 5 = 𝑥 − 1
4. √3𝑥 + 7 +2√𝑥 − 8 = 0

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Example 2
Solve the equation √𝑥 + √𝑥 + 3 = 3.

Exercises 5–6
Solve the following equations.
5. √𝑥 − 3 +√𝑥 + 5 = 4 6. 3 +√𝑥 = √𝑥 +81

Lesson Summary

If 𝑎 = 𝑏 and 𝑛 is an integer, then 𝑎^𝑛 = 𝑏^𝑛. However, the converse is not necessarily true. The statement 𝑎^𝑛 = 𝑏^𝑛 does not imply that 𝑎 = 𝑏. Therefore, it is necessary to check for extraneous solutions when both sides of an equation are raised to an exponent.

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