Extract a Perfect-Square Factor
A nonnegative radical can be simplified by separating a perfect-square factor.
About 25 minutes, plus any extended practice
Open lesson 1Algebra2: Radicals and Complex Values
Root expressions can be simplified through perfect-power factors and rational exponents. Squaring equations can introduce extraneous candidates, while complex arithmetic extends the number system using an imaginary unit with square negative one.
Before you begin
- Factor perfect squares and cubes; use integer exponent rules; check equation solutions by substitution.
Choose by skill rather than age alone. Read with an adult when useful, revisit a lesson, or explore another grade.
Follow the lesson sequence
Interpret a Fractional Power as a Root and Power
For the positive bases here, an exponent m/n means take an nth root and then an mth power.
About 25 minutes, plus any extended practice
Open lesson 2Reject a Candidate with the Wrong Original Sign
A principal square root cannot equal a negative real number.
About 25 minutes, plus any extended practice
Open lesson 3Multiply a Complex Number by Its Conjugate
A conjugate pair differs only in its imaginary-part sign.
About 25 minutes, plus any extended practice
Open lesson 4Review and transfer
After the lessons, try 4 new review cases and a practical task. Each answer has an explanation and a link back to the related lesson.
Open the unit reviewGuest answers are temporary. Keep your own paper or document; this unit does not certify completion or record a school grade.
Topic references
- OpenStax mathematical topic reference: topic reference — Algebra2: Radicals and Complex Values
These references informed the topic selection. They do not certify complete standards alignment.