Pre-Calculus 11 Notes

By: Gen L.

Lesson 1: Working with Radicals

What is a Radical?

• Radicals () can be treated very much like fractions. They can be simplified into lower terms, and this is how we ALWAYS want to present our answers.
• Example Radical:
  • : Index (, number of times is multiplied by itself to get )
  • : Radicand (value when is multiplied by itself times)
  • : Radical (The full expression)

Key Property: Radical Multiplication

• if is a natural number, and & are real numbers.

Converting Entire to Mixed

• Example:
  • What are 45's factors, one of which is a perfect square?
    • ? That works.
• This even works for higher indices.

Example: Entire to Mixed

Examples: Entire Mixed

• Simplify
  • How many groups of 's are there?
• Simplify
  • How many groups of 's are there?

Converting Mixed Entire

• Example:
• Also works for higher indices.
• Example:

Examples: Mixed Entire

Adding / Subtracting Radicals

• Summary: Combine Like Terms!
• Whenever we add radicals, we need a common denominator. We need to convert into mixed radicals with the same radicand, then add / subtract the whole numbers out front.

Examples: Adding / Subtracting

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