Solving Radical Equations
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Common Core For Algebra
Solving Radical Equations
Student Outcomes
- Students develop facility in solving radical equations.
New York State Common Core Math Algebra II, Module 1, Lesson 29
Classwork
Example 1
Solve the equation 6 = 𝑥 + √𝑥.
Exercises 1–4
Solve.
- 3𝑥 = 1+ 2√𝑥
- 3 = 4√𝑥 − 𝑥
- √𝑥 + 5 = 𝑥 − 1
- √3𝑥 + 7 +2√𝑥 − 8 = 0
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 𝑎𝑛 = 𝑏𝑛. However, the converse is not necessarily true. The statement 𝑎𝑛 = 𝑏𝑛 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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