6.2 – Simplified Form for Radicals Product Rule for Square Roots Examples:

6.2 – Simplified Form for Radicals Quotient Rule for Square Roots Examples:

6.2 – Simplified Form for Radicals

6.2 – Simplified Form for Radicals Rationalizing the Denominator Radical expressions, at times, are easier to work with if the denominator does not contain a radical. The process to clear the denominator of all radicals is referred to as rationalizing the denominator

6.2 – Simplified Form for Radicals Examples:

6.2 – Simplified Form for Radicals Examples:

6.2 – Simplified Form for Radicals Theorem: If “a” is a real number, then 𝑎 2 = 𝑎 . Examples: 40 𝑥 2 𝑥 2 −16𝑥+64 18𝑥 3 −9 𝑥 2 4∙10 𝑥 2 𝑥−8 2 9𝑥 2 2𝑥−1 2 𝑥 10 𝑥−8 3 𝑥 2𝑥−1

6.3 - Addition and Subtraction of Radical Expressions Review and Examples:

6.3 - Addition and Subtraction of Radical Expressions Simplifying Radicals Prior to Adding or Subtracting

6.3 - Addition and Subtraction of Radical Expressions Simplifying Radicals Prior to Adding or Subtracting

6.3 - Addition and Subtraction of Radical Expressions Simplifying Radicals Prior to Adding or Subtracting

6.3 - Addition and Subtraction of Radical Expressions Examples:

6.3 - Addition and Subtraction of Radical Expressions Examples:

6.3 - Addition and Subtraction of Radical Expressions A Challenging Example 2 𝑥 2 𝑦 4 𝑧 3 1 5 2 𝑥 2 𝑧 3 2 1 5 𝑥 2 5 𝑦 4 5 𝑧 3 5 2 𝑥 2 𝑧 3 2 6 5 𝑥 12 5 𝑦 4 5 𝑧 18 5

6.4 –Multiplication and Division of Radical Expressions Examples:

6.4 –Multiplication and Division of Radical Expressions Examples: 𝑥− 3𝑥 + 5𝑥 − 15

6.4 –Multiplication and Division of Radical Expressions Examples:

6.4 –Multiplication and Division of Radical Expressions Review: (x + 3)(x – 3)  x2 – 3x + 3x – 9  x2 – 9 𝑥 +3 𝑥 −3 𝑥 2 −3 𝑥 +3 𝑥 −9 𝑥−9

6.4 –Multiplication and Division of Radical Expressions If the denominator contains a radical and it is not a monomial term, then the use of a conjugate is required in order to rationalize the denominator. conjugate

6.4 –Multiplication and Division of Radical Expressions Example:

6.4 –Multiplication and Division of Radical Expressions Example: